Alright kids, strap yourself the **** in.
i'M FLYIN' THIS BABY
TO DA MOOOOON
"The real purpose of Pokemon Centers is not to heal Pokemon, but to stunt their growth."
Think about it. It's eminently clear that Pokemon in the wild grow and evolve much faster than tame Pokemon. What do all trained Pokemon have in common? Inevitably, trainers have to bring their Pokemon to Nurse Joy for healing — treatment which is suspiciously free, which must mean it is subsidized by the government. Indeed, almost everything happening in that world is the result of a Goverment conspiricy to deal with the existence of creatures of such incredible power. The idea of letting kids run around the country battling wild animals is a way of keeping the Pokemon population from growing too powerful. But that opens the door to Pokemon trainers directing their powerful pets against the government; hence, Pokemon Centers inject the Pokemon they treat with chemicals to inhibit their growth, and the sport of trainer battles — essentially legalized cockfighting — is formalized as a distraction from the true potential of Pokemon.
Pokémon Battles were designed just so Trainers would be forced to go to Pokémon Centers.
Alternatively, the Pokemon have, by and large, gotten into the habit of holding back, especially around humans, with the intent of preventing serious injury or worse. This explains the exceptions much better - the most obvious being the Genetic Pokemon Mewtwo, who in the first movie is clearly shown fighting over and over (and thus getting healed over and over) but still displaying disproportionately high power.
In Diamond/Pearl, it's actually *canon* that Poke Balls act as a Power limiter. Team Galactic needed a special device in order to control Dialga/Palkia at full power. If they had used a Poke Ball, it wouldn't have been able to create a new universe for them.