Oh boy, symbolism!
I think it's really interesting how the main series handled what the game mechanics are saying recently. In gen 5 there was a whole antagonist who's goals felt really relatable in a way, because when they said Pokemon battles are violent and trainers can be cruel, it's entirely right; the mechanics of battling spell that out all the time (Fighting opponents to fainting, abandoning Pokemon to the PC and never using them ,the fact that Pokemon will allways obey unless under special circumstances)! Of course there are also mechanics like Happiness, saying that Pokemon are friendly creatures who form real bonds with their trainers, and features like Contests/Musicals, Following Pokemon, Triathelon, Pokestar Studios, mini games and dress up games, and feeding treats like Pokeblocks/Poffins all allowed the player to interact and bond with their pokemon in ways that aren't violent, and that was emphasized even more in the next generation with Pokemon Amie.
Personally I'm a big fan of the new Affection feature having an affect on battles; suddenly there's new flavor text, and a loyal Pokemon shares a glance with its' trainer before getting a critical hit or surviving a knockout blow...and then after the battle it can be petted awww! Gen 7 took it even further with grooming after a battle, in special ways dependant on what kind of battle just took place. While nothing about the Pokemon Amie/Refresh mechanics are essential to the core gameplay, tying the cute bonding aspects to the more violent battling side really makes Team Plasma back in gen 5 seem less credible.
That ramble might have been more about meaing assigned to mechanics than their actual symbolism....Okay, representation.
Something easy to break down I think is breeding. Keeping the same mechanics, it's not really different from a fusion system where the player gets to keep the components. But framing it as breeding and producing eggs is a little friendlier, because it frames the pokemon world as a little more grounded than say, if 2 pokemon were stuck in a special PC box and the player then had to wait 2 minutes or pay to skip while the PC copied, combined and duplicated the Pokemon's data.