Should most trainers ask?

I know trainers serve as both: a way to ensure that the player will level up/is good enough to go on and to render the area less short/harder to go from point X to point Y.

But normally, should be there more interaction, can a trainer decline a fight? I'm sure in anime it happened but is there any rule I'm missing?
And if a fight could be declined, would you guys prefer a game which adds the possibility to decline (most) fights or prefer it the "vanilla" way?

See, the thing is I'm totally fine with the "trainers not being able to reject Pokémon Battles" thing but I should think that there could be a bit more complications:

1) I wish we can lazer-eye trainers and battle them and see their already weak Pokémon faint, not like the VS Seeker and variations where we can only battle trainers if they're ready. They certainly never ask us, so why not the other way round? (Could help us a lot in training also)

2) I wish we get some time before the trainers lock us on, so that it would be more "realistic" the way the battle starts. I mean the OW scene of course, because there's no way the two trainers magically warp into a battle ground with lots of space and get some distance between each other. This could possibly relate to using the environment in battles. Also maybe shoo him off to a Pokémon Center once he's beaten, that's a twist.

3) Third thing is, I don't want them to jump in and say, "I like shorts! They're comfy and easy to wear!" and battle us. It's a bit weird the way he tells a random statement and immediately battles us, at least let him tell us his name and say a "let's battle!" variant (though some people do, most don't).

When I write fanfics or RPs, I usually end up explaining it by some trainer's unwritten codex. You have to accept a challenge. When two trainers meet, a battle must start. You can't harm a trainer physically if they own pokemon etc. Rules to make pokemon a bit mysterious yet explain the game mechanics in a satisfying enough way.

I think it works well in the games as it is, as the ability to decline any challenge would make things a bit too easy.

It would be nice having an option to refuse trainer battles, but I think most people would take advantage of this feature, sort of, and keep declining when NPCs challenge them. This would have a bad affect on them on them though, as it'd cause their Pokémon to be under-leveled, giving them a hard time when it comes to facing gym leaders, rivals, Elite Four members, etc. etc. d: Also, we already have a way to avoid trainer battles—by trying not to make direct eye contact with them and finding another way around the trainers. If we were ever given the choice of declining trainer battles, then it would take away all the fun of trying to dodge them and give us an easy way out.

In the 'real world' of Pokémon, so to speak (fanfiction and such), I think it would be pretty reasonable for Trainers to be able to decline battles. In terms of the games, however, which are meant to pose a challenge to the player, you should not be able to; as Perdition Haze mentioned, there are ways to get around it anyway, and part of the point of enemy Trainers is to get you to the point where you're thinking, "Oh god, I've gotta get to the Pokémon Center, I don't know if I'll be able to go on much longer without-- NO YOUNGSTER JOEY I DO NOT WANT TO BATTLE". And then you have to fight Youngster Joey and his top-tier Ratatta with no Potions and a Chikorita with 5 HP.