Do you battle all trainers in the games?

I do, although I'll sometimes skip trainers so I can go back and battle them with Pokemon I have yet to add to my team, because grinding in the grass, or baiting and switching against stronger trainers, takes about twice as long as just straight-up battling a trainer with Pokemon around the same level.
 
I try to fight them all if I can. Gimme that EXP! Though I did have a funny encounter in Sword recently where I skipped an early route trainer by accident and came back to face his level 13 Budew with my level 94 Galarian Rapidash. Oops.
 
I battle most trainers in the game. I usually skip a few (usually the trainer classes that I like; this might sound weird but I feel guilty about defeating some of them) but for the most part I want all the money and experience I can get.

I'm also known to leave some trainers in order to have a Pokemon I catch later on battle them to help them get up to the same level as the rest of my team.
 
I'll be honest No
I'd rather run away from them
but then again I have 2 legendary's soooooo
 
The way I play it is usually adviced to battle as many trainers as possible. That is: when you try to beat the games without grinding and with a fully realized job driven party consisting of Pokemon of any type of viability it helps if you take on any trainer in terms of more EXP and money.
 
i battle the majority of them. some of the ones i skip if i can't be assed to (like if im rushing towards a gym or something) but for the most part, i battle most trainers i come across.
 
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