There has nothing that has been shown that pokemon legend or not parish because they are captured and not "free".
He likes a lot of pokemon, but that doesn't equate to his capturing them. Like Ash was trying to go on a catching spree in Viridian Forrest but he only got Caterpie and Pidgeotto. He was seen wanting a Weedle but the writers didn't allow it. So I think it is more about what they want for him which they write into his character.
He is given pokeballs and if that was an issue he could go to the mart and by new ones. Pokeball availabity I don't think has ever been an issue.
I never saw how Team Rocket would inhibit his capturing of pokemon. Especially now a days when they are seen few and far between.