Another thing to keep in mind, even outside of ribbon accomplishments, is the more simple fact of having a mon in the newest game compete in and perform certain side content. Even if these mechanics weren't major in any way, having my favorite Azumarill compete in things like the Pokeathlon, PWT, and use Mega Evolution in ORAS was all something very satisfying to see happen. Without transfers, new memories and functions can't be made with your old favorites.
From a trading standpoint, it completely spins the system on its head. While Pokemon Home allows you to trade any Pokemon with others who have Home, the inability to use a Pokemon outside of a certain game's regional dex creates problems regarding a Pokemon's value. Why would I want someone else's Swampert, if I'm not even sure if they'll ever be usable anytime soon? Because of this system, it becomes very difficult to gauge the value of any Pokemon outside of the newest games.
And from a battling perspective, both casual and competitive, it has its issues, but I'll focus on a more casual one. Let's say you and a friend wanted to battle, 6v6, using all of your favorites. Because of the lockout, such a thing becomes an impossibility, when back in Sun and Moon, any mon, whether they be from Sevii Islands or a new Pokemon caught in Alola itself, can be used against each other. With this gone, you're no longer able to assemble a team of everyone you love. While it's likely that one'd be able to assemble 6 different favorites, teambuilding still suffers a lot. What if I liked Corviknight, but also wanted to use a Houndoom on my team? How long would it take for a game to exist where both of them are in the same region? And will I be able to use the others, too, or would they need to be compensated and replaced?
In any case, while not everyone transfers their Pokemon, it is definitely an important feature to keep in, and sets Pokemon as a series apart from any other Monster Taming franchise.