He didn't say it wasn't illegal or frowned upon, only that it was easier. Especially the collapsing Pokeballs we see later in the movies that are half the size of the conventional pokeball when not in use.
This. Pokeballs have been shown to be able to shrink to a much smaller size than an handgun
Even if it's true most of their members The government would have strict licensing policies for owning and keeping Pokemon, and would keep a very, very close eye on any pokeballs on someone's person at all times. In fact, it would probably be entirely illegal to walk around in public with pokeballs on you except under super specific circumstances. Think about it, you say that a Pokemon is just as deadly as any weapon in the right hands. In fact, a Pokemon can be 100s of times more deadly than an assault rifle or dirty bomb in just about anyone's hands. In the right hands, the right Pokemon can level a city.
Those are however still important points to discuss.
-Walking around with pokeballs but not a pokeball license shouldn't indeed be allowed. People need to register any pokemons they own/evolve at the nearest pokemon center and get licenses.
However, you can still walk with dangerous pokemon with you (and actually let them tag you behind in the street to show off) because besides guns and pokemons, Earth is also filled with psionics. Sure your Gyarados can wreck the city if you let it loose, but that other guy may do just as bad just by thinking. The Pokemon League fought hard on tribunals to allow their trainers to carry their pokemons with them all the time for "self-defense and that of their neighbours".
-On the other hand, even some smuck lv1 NPC can use an assault rifle or even a prototype laser pistol, but a lv1 trainer can only get the weakest pokemon to obey it. City-leveling pokemons like a Gyarados can only be controled by an highly skilled trainer, and you'll have a considerable hard time to reach that kind of status whitout your face being well known by most people in the world.
I imagine public ownership of Pokemon that have powers more deadly than, say, a handgun would be greatly restricted, and carrying any such Pokemon in a pokeball would almost certainly be strictly forbidden. Permits might exist (in the form of Badges?) that allow private citizens access to more dangerous Pokemon, but again keeping them in pokeballs is the equivalent of allowing concealed nuclear weapons. Remember, in the real world, we go to war against nations that attempt to conceal nuclear programs and we straight up kill individuals with access to nukes without even bringing them to trial.
Eerr, last time I checked the exact oposite hapened. The USSR got nukes? Cue half a century of stare-down, and Russia still has nukes. Iran and North Korea have concealed programs? Lots of threats, but no actual war (and NK actually gets some freebies in between). China probably isn't also telling us even half of whatever research they're actually doing in nuclear. Meanwhile Lybia leader gave up on their nuclear program a few years ago? Send in the bombers! Iraq never had one? Send a full assault!
Thing is, having nuclear weapons (or equivalents) makes for an impressive deterrement for people to attack you. Threat of mutual anihilation and all that stuff. It's the exact oposite, not having nuclear weapons at all (or a friend with them), that makes you an easy target.
Plus nuclear weapons demand rare materials and extensive resources. Dangerous pokemon are literally growing in the trees.
So in this pokemon case the government may've indeed tried to turn dangerous pokemons illegal under strict conditions at some point in history, but in the end dangerous pokemon grow in the wild, Gyms and trainers like to have their own autonomy, and the military was already kinda too busy fighting off actual rampaging wild pokemon to go after trainers that can actually keep their destruction machines in check, if not using them to help save the day. It's a delicate balance yes, but basically trainers get to keep their dangerous pets as long as they don't raise too much ruckus in civil areas. Luckily, most Gym leaders do have morals and police their own area and students (because there's no glory on ruling over a dead wasteland), and again the Elite Four quickly intervenes whenever things get too nasty. It's more like a "bigger fish" policy. You may have a strong pokemon, but if you stand out too much, there's an even stronger pokemon at the next corner, so you want to be friends/neutral with them, not murdering enemies.