Apologies in advance for the wall o' text, but the topic of Vancian casting vs. alternate systems is one that's near and dear to my heart.
Considering that various campaigns I played started at level 1 and ended at level 3 or 4 (and, again, rarely went beyond level 6)
At lowish levels (1-9), Wizards were more favorable. They had fewer spell slots than Sors, but their day-by-day repertoire flexibility mattered more.
Only after playing a Druid from level 1-11 did I realize the power of spontaneously-cast spells.
While you toss in the topic of level ranges as an aside, I think it's actually key to why you might feel spontaneous casting is better and more fun overall while the forum consensus is the reverse.
At low levels (1-5 or so), prepared is nearly strictly superior to spontaneous, because (as you noted) with only a handful of spells available spontaneous casters get pigeonholed pretty hard and getting access to the key boosts of 2nd- and 3rd-level spells a whole level ahead of time is huge. Then at low-mid levels (5-10 or so) spontaneous casting suddenly starts to look a lot more appealing, because both prepared and spontaneous casters have "enough" spell diversity and spell slots to get by most days, the relative combat power boost of 4th-level spells over 3rds is nowhere near that of 3rds over 2nds, and you start having enough gold to spend on wands and scrolls to cover a lot of the utility gap. For folks who mostly end campaigns in the low-mid levels, I can definitely see why a lot of people gravitate to spontaneous casters over time.
But the thing I think you're missing is that at the high-mid and high levels, things flip back
to favoring prepared casting. 5th-level spells shine for their utility, not their combat power, so a Wizard 9 having a single 5th-level spell where a Sorcerer 9 has none isn't really a big deal (e.g. you can always get a scroll if your 9th-level party needs to teleport
somewhere) but a Wizard 14 having a bunch of 5th-level utility slots while a Sorcerer 14 has just 3 5th-level spells known which are likely to be more combat-focused actually is a pretty huge deal. Reliable divinations start to come online, so the ability to predict challenges gets much easier and the effectiveness gap between a spontaneous caster's spells known and a prepared caster's generic daily loadout narrows considerably. High-level play starts to revolve around having layers of buffs and access to broad utility, something spontaneous casters have difficulty keeping up with because they can't just dedicate 1/3 of their daily slots to that and have the rest of them for combat--and consumables for mid- and high-level spells are increasingly expensive and aren't sustainable to use every day, so you can't just buy lots of scrolls and wands to cover gaps anymore. And so on.
You're definitely right that there's an issue with "forum logic," but it's not that it's all handwavey theorycrafting, it's that people just repeat "wizards > sorcerers" as a shorthand because they're talking in generalities, without getting into the fact that the degree to which that's true varies by level range, type of campaign, and so on.
It's much like how the Tier system aggregates many different optimization levels and people who just rely on that and don't get into the nuances often argue it's all theorycrafting and doesn't match their experiences. At newb optimization levels where new players don't have a good grasp on what spells are good, what kinds of challenges they'll face, and the like, wizards are bad and sorcerers are utter shit because a sorcerer's bad choices haunt them forever but a wizard can fix their issues with a bit of research. At low optimization levels where blasty wizards and healy clerics rule the roost, sorcerers are great and wizards are meh because the party casters are only doing one or two things anyway so spamming spells is king. At moderate optimization levels where players start fiddling with minionmancy and seriously using divinations, wizards and sorcerers are mostly on par because, again, there are only one or two tricks in play but the wizard can get a bit deeper and broader with each. At high optimization levels, wizards leave sorcerers in the dust for obvious reasons. Yet if a new player just looks at the Tier system that says wizards are T1 and sorcerers are T2 so obviously wizards are strictly superior, they'll miss that detail and not get why their 5th-level evoker is falling behind their buddy's 5th-level summoning-focused sorcerer.
I have a lot of personal experience with the prepared-vs.-spontaneous-at-various-levels issue, since nearly all of my campaigns run the full gamut from low to high levels instead of running into the (apparently common) phenomenon of dying out around mid levels; in the past decade, 80% of the campaigns I ran made it to 18th level or higher, and the lowest level any of them ended was 12th. Several of my players started off always playing prepared casters because they were "stronger" or always playing spontaneous ones because they were "easier," but as they got a feel for the playstyles at different level ranges they've all gotten more comfortable mixing and matching based on what the starting level will be, what their concept is, and so on.
Dwelling on the possibility of power is often more appealing to theorycrafting and dreaming than the likely reality of what people face. Being able to change what spells you have available to you every time you prepare spells (normally daily) can be a huge boon, but, at least in my experience, people don't play that way. They pick a certain number of favorite spell preps on a near-daily basis (like grease and enlarge person every day on a Wizard) and might swap out a spell or two per spell level to do something different (like preparing color spray one day and magic missile the next). In short, prepared casting focuses on what you can be while spontaneous casting tells you more of what you are.
This is a bit of a misunderstanding about the benefits of prepared casting. Having a standardized spell loadout is totally fine and fairly common; a wizard who completely shuffles his spells every day is likely ditching effective spells for no reason, and the benefit of being able to change just one or two spells each day is overrated. It's the ability to have one standard loadout for adventuring and a completely different one for downtime that really matters.
You mentioned Red Hand of Doom, which is a good case study because it starts and ends in the "wizards > sorcerers" range but plays through the "sorcerers are more fun than wizards" range. If you know that you're heading into a Red Hand of Doom game, your party wizard and party sorcerer are probably going to have very similar spells available most of the time: there are lots of large groups of goblinoids so load up on AoE blasting, there are lots of dragons so pack energy resistance buffs and anti-flyer spells, and so on. But where the sorcerer is stuck with those spells every day, the wizard can take a downtime day to completely swap those out for scrying
to try to figure out where the Red Hand forces are, animate dead
to get a bunch of hobgoblin skeletons as meat shields (er, lack-of-meat shields), sending
to be able to update allies at long distance rather than flying back and forth all the time, and so on, and then go right back to a combat loadout the next day--to say nothing of scribing a scroll or two or crafting a wand to allow more divining or reanimation or whatever on combat days.
A single day of the wizard's downtime casting every in-game week or so can make an incredibly dramatic difference at the campaign level even if at the tactical level the wizard and sorcerer play identically and even if the sorcerer largely edges out the wizard on the firepower front. And of course if the party successfully finishes Red Hand of Doom and the DM says "Congrats, you saved the country from Tiamat's armies of goblinoids and dragons, but now she's made a deal with Bel and there are armies of devils invading your world!", it's easy for the wizard to pivot from the fireballs
and energy resistance buffs that are good against dragons to the lightning bolts
anti-teleportation/-scrying wards that are needed against high-CR devils, while the sorcerer is stuck with what he already has.
There's more than one way to play any edition of D&D, and I felt that spontaneous casting is the better, more fun, and more convenient way to handle casting.
Don't get me wrong, spontaneous casting is
generally more fun if you don't like the bookkeeping, and on the rare occasions I get to play instead of DM I, too, try to get some amount of spontaneous casting on my prepared casters so I always have fallback options when something unexpected comes up. But I think by singing the praises of spontaneous casting over prepared you're swinging the pendulum too far in the other direction.
WotC eventually implemented spontaneous casting of sorts as standard for every casting class in D&D 5e, at least in the 5e PHB. (Prepared casters chose a certain number of spells/spell levels to prepare and cast them spontaneously. Fully spontaneous casters remained fully spontaneous with limited numbers of spells known.)
I see this comparison a lot--"5e went more spontaneous and everything got better!" and the like--but it's flawed for a few reasons. First, it's no longer comparing prepared to spontaneous, it's comparing a best-of-both-worlds pseudo-Vancian setup to plain ol' spontaneous, so obviously that version ends up looking better.
Second, the change was necessary due to how casting in general changed in 5e. If you're going to require people to heighten spells to be relevant instead of auto-scaling by CL, you obviously can't require people to prepare everything at the beginning of the day, just like how 3e psionics has condensed powers and augmentation because of the differences between power points and spell slots, and just making psions prepare powers or letting wizards use spell points would be a total non-starter.
And third, most of the comparative benefit of prepared casting goes away in an environment where spell selections are incredibly limited, good utility spells are heavily nerfed, removed, or nonfunctional, and all the downtime spells you care about can be cast as rituals anyway. It's much like how a wizard is going to end up a lot closer to a sorcerer both power-wise and spell-selection-wise in a 3e core-only environment where the DM bans polymorphing, teleportation, and permanent minions and there's basically no downtime between adventuring days: if there's very little actual benefit to being able to swap out your spell loadout from day to day, then obviously picking that benefit over in-combat flexibility is a sucker's bet.
As a side note, 5e pseudo-Vancian is much like the 3e spirit shaman's spellcasting mechanic, and one would think that a class that's "druid, but with more flexible spellcasting" would be obviously better than the druid, yet we know that the druid ends up being far better because while its casting method is indeed better the advantage of Wild Shape and an animal companion over a grab-bag of spirit-related class features outweighs it in practice. Likewise, while spontaneous casting is basically "all the good spells the wizard wants to prepare anyway, but with more flexibility" in a bunch of circumstances, you need to take the full context into account when determining which one is better on the whole.