In the anime, whenever they trade pokemon, they always use this superfluous machine that exchanges the two pokemon’s pokeballs. I know this is meant to emulate trading methods in the game (as a machine in the pokemon center is needed to trade). In the the anime this could be because the pokeballs need to be re-registered, but there are also parts in the anime where pokemon are just given away without a machine. So why is a machine needed for trading, but not for giving away a pokemon?

I suppose it might be that the point of the machine is actually to move the Pokémon themselves from one Pokéball to the other – we know that Pokémon in the anime do seem to be tied to their own Pokéballs (take, for instance, Pokémon Food Fight, when Ash has to drag Snorlax over a mountain because his Pokéball is broken – for whatever reason, he can’t just, say, stick Snorlax in Pikachu’s Pokéball for a few hours).  When you give a Pokémon away, you normally give away the Pokéball with it, so you don’t need a special machine.  Of course, that just raises the question of why they’re so damned possessive about their Pokéballs that they aren’t willing to let them go when they make a trade.  Could be some sort of weird throwback to a period when Pokéballs were rare and valuable artisanal objects – before production was automated and standardised, they might have been covered with valuable decorations, or emblazoned with a noble trainer’s crest, so that traditionally trainers would want to keep their own Pokéballs even when trading their Pokémon away.  Basically the machine’s function is actually completely insignificant for the vast majority of people, but they use one because that’s how trades have always been done.