Brainpiercing, essentially what you are saying is that because attacks of opportunity can kill at 1st level I shouldn't try to create a universal rule that allows them to be more deadly at any level beyond 1st level? That's how I'm reading your post anyway.
No, I'm saying they should not be more deadly without investment. Because this game is ALL about investing your character resources into a functioning package, at least on the build side of things.
Any basic ability that goes without investment should be balanced for level 1. It might scale, but that's another story.
Your bullet list is basically fine, BUT I don't think any of those points is a dealbreaker for me. Because basically, no investment equals no return. I'm not saying all is perfect, but anything added should require an investment.
You'd have to rewrite weapons so that they all only dealt 1 dice worth of damage at 1st level (so no more 2d6 Greatsword, sorry), but the pay off is that at every odd threshold of BAB you attain beyond +1 you get an extra damage die with your weapon attacks. So, at 3rd level your Longsword deals 2d8 base damage. At 13th level your Halberd deals 7d10 damage.
Ok, so there's a disconnect here: You're saying that at level 1 you can kill a guy with one hit (1HD vs 1 damage die), so let's just change nothing else except weapon damage to make sure that I can do this at any level. I'll grant you that's oversimplifying, but effectively this will happen - both ways. Now let's see: A CR 7 Bulette deals 2d8+8 with its main attack. But going by your rule, and using its BAB of 9 (and the only sensible way is to run it consistently) it will now deal 5d8+8. That's not a complete game-breaker, but still an average 15 damage more - on up to 4 attacks. So the critter deals 12 dice more damage, vs. 6 HD above level 1, which average 30HP for a D8 character, excluding Con. That does make the game very deadly. And it's not like people won't want to build a Hood or Ubercharger just because their weapons now deal more damage.
The other problem is how to consistently adjust your damage dice? You said BAB, but that can be very dangerous to PCs, because a lot of monsters have a lot of HD and good BAB. One might suggest CR, but that's a wonky concept in itself, and everything will have to be re-examined for such a change. The other option is HD, but then those high HD low CR monsters will suddenly deal a crapload more damage.
The next problem is many attacks - if you dealt four times 1d4 originally, but now you are dealing four times 4-5d4, that's much bigger increase than the dice a general character gets for his iteratives. Granted, here both druids and wizards have a BAb problem, and Clerics have a polymorph problem. But it just might make sense to play lots of Thri-keen now. At high levels everyone could get access to divine power, so a polymorphed wizard will again outperform the martial types in their own area of expertise.
And in addition to just scaling damage you have now removed weapon size categories - a colossal weapons deals the same single damage die at level 1 as a tiny one.
Scaling base damage by level or BAB is a good idea, let's work on the amount.
I also feel this goes very much into "pseudo advancement" territory. What I mean by that is that your character gains levels, but gameplay stays basically the same. Generally D&D advances from basically death roulette over ablation into rocket tag. With your changes it would go from death roulette straight to rocket tack - for meleers, too. With the exception that it might include some anti-rocket-rockets, too.