As our world is now, I think it would be...difficult. Dunno, I'd say training allowed with 14 or so...You could say everyone has to do a test to get the licence. This would be the test to prove if one's ready, right?
The troublesome is that school is obviously more important in our would than in the Pokemon world.
However I think it would be cool. Okay, we wouldn't have Pokeballs (since I think they would be difficult to invent...no apricocos to start with)
Maybe our nature would chance, because Pokemon would fill the ecological niches of the animals...we would have to think about the question if people eat Pokemon again...on the other hand, human couldn't desttroy the nature so much (deforest etc) because who would dare to intrude a forest with dangerous...bedrills or whatever could live in it...they couldn't work there.
Also, I'm sure organisations like...greenpeace or something wouldn't like us to use Pokemon for fighting.
By the way:
But in places like Germany, there is no drinking age, and therefore, it is abused less by a substantial amount.
The drinking age here in germany is 18 and it's pretty much abused... and so would be Pokemon. But if everyone (or almost everyone) would have one, it would turn out to be balanced...maybe.
However, as long as I could have a Chimecho, I'm fine with everything :D