Realistically, it's a limitation for video game purposes, and a limitation of the time. RBY probably couldn't process you holding dozens of Pokemon in your team, and it wouldn't be fair to have too many fighters in reserve to steamroll whatever stood in your way. Imagine how trivial gyms, the E4 and Champion would be if you could hold a team of fifty.
In terms of a world where people would act this way, it's probably a kind of honour code. You only carry a certain number of Pokemon, you do turn based combat, and you only battle to the point of fainting. Like, jousting and fencing and sparring and boxing all have their rules, even though you're taking weapons/fists to another person with the capability to kill, you respect your opponent and have a good clean match. I don't know the ins and outs of cockfighting or dog rings, but they probably don't fight to the death or dogpile a bunch of animals multiple-on-one either.
There's nothing actually stopping someone from possessing a greater amount of pokemon (whatever evil team thieving a bag full of other trainer's pokeballs, pokemon centers and professor oak and the charicific valley and daycares and ranches and all other kinds of facilities that hold large amounts of pokemon) and there's nothing stopping anyone from using a larger number of Pokemon in battle (doubles, hordes, that one dickhead at the start of the first movie going 3-on-1, every time ash & company get accosted by an enemy and use every pokemon they have to fight back, etc).
