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There would definitely be huge regulations on breeding. Overpopulation would likely be a serious problem and culling would be necessary.
Battling likely would also be regulated. You can't go around fainting and possibly killing all the wild pokemon in the area.
I doubt the pokecenters would be free, that's all lot of money with no real return except maybe donations.
Nukes I think would be obsolete; pokemon are seen as more sentient than most animals irl and killing all of them in a large area I don't think could ever pass through government. Guns might still be around. You don't really have to tell a gun to kill something and it's quick if you have good aim and it can't disobey you.
A gym-like system would probably be in place to test the strength of locals. They have varying levels meaning you can train there for a while. The school system would probably be in place.
Life would be so much cooler though.