Eeeh... I'm not sure I really buy entirely ignoring the PWTs existence.
Not its existence, its canonicity. It still exists, but whether the PWT with participants such as the protagonist (being the champion), Red, Giovanni, etc participating isn't necessarily canon. Quite a few number of fans are still debating this, though nothing official's been said.
You can't just shoot a person being protected by a pokemon. Their pokemon protects them and you're forced to deal with the pokemon. Even if you could, that is still a job accomplished much better and more reliably by a pokemon. Why would humanity spend all that time perfecting a complicated tool like a gun when they are -completely- outdone in every imaginable way by pokemon? Before they'd even be able to get to semi automatic rifles that aren't really useful they'd have to evolve their technology past muskets and stuff that are even less useful.
Because humans need things to protect themselves if they don't have pokemon on them. In the games, most trainers that are out and about only have 1-3 pokemon, save for Ace Trainers and the protagonists (so basically, anyone going for the Pokemon League). There's a very real chance that a trainer's pokemon will be fainted and they won't be near a pokemon center.
In the context of war...just shoot the person. A person riding on a charizard is basically the same as a person riding on a mount in any other setting, and they can still be shot. Pokemon aren't wearable weapons or armor after all, the humans won't be invulnerable simply because they have pokemon with them. Commanding pokemon might not always be the most practical course of action in various cases, especially one is going for covert or instantaneous tactics. It's unlikely that they would start in the primitive stages of firearms that we did because they already have other pieces of technology, and even pokemon attacks, that could be used as models that may reflect or even transcend our modern firearms.
Y'know what makes a lot more sense? Explosives. You can make traps with explosives and they don't require much advanced technology. They also have other uses outside of getting people hurt. Even a knife makes more sense than guns because you can use it for -other things-.
Mmm...I dunno. Explosives would be viable, but that's assuming the one arming the bomb has both the field advantage and time to arm one. If we're talking grenades, they could carry them, but they're not as reliable, nor as easy to use, as guns. They could carry knives, but we'll simply go back to what you were saying before: the humans would be protected by pokemon. Hitting a person with a grenade or a knife while they are riding on a blitzle, possibly armed themselves, is MUCH harder than simply shooting those same people. Plus, you could have grenades, knives, AND guns. In fact, that seems like the most practical courses of action. Not only would being armed with those weapons be relatively lightweight, but it would also be incredibly handy in combat.
As for armor... Yeah, I could see people using armor in the pokemon universe, but not traditional armor like in real life. That just wouldn't make a difference without some fictional supermetal being introduced. What I could see is armor to protect people from environmental hazards. Like, masks designed to keep wayward spores out of your nose/mouth and waterproof clothes because being soaked by splattering water can only make things worse. Things like that.
Humans are not only tacticians but also soldiers. They have available materials for making stronger armor, and that's pokemon, they're skin, they're steel, and their other various body parts. Sure, those environmental hazard prevention apparatus could be worn by people, but they should be worn under their armor. After all, the generation killing war was a generation killing war because the adverse effect it had on young-middle aged men was devastating. They no doubt fought on the front lines as well, and thus, it was very likely that they had armor strong enough to withstand the strength of various pokemon attacks which, considering the materials they had at hand and the rate at which technology is developed in the pokemon universe, they very likely did.
Same for firearms, really. They most likely made firearms, probably using various projectile pokemon moves as a model, and made them efficient enough to be effective against pokemon.