I see the other TR members outside of Giovanni & Matori, the same way I see on Brock & Misty, they had their time and the anime wanted to move on with new main/important characters. I think there's would be similar results if there's more feud between TRio and the regional criminal teams.
I guess I think this sort of same-field rivalry has more potential because of the more personal resentment that could be involved. With the other villain teams, some of the rivalries can be fun but they're mostly just impersonal hinderances towards each other. While TR members within the same field would have a reason to hate Jessie and James on a more personal level now, since they're at least halfway successful now despite barely doing anything more than before. Butch and Cassidy and Domino hated them before but it was more just a one note bully antagonism where they picked on the weaker litter, the trio weren't really doing anything to them first, they were already exposed as washouts, they were kicking them while they were already down. It was a fun standard 'eviler common enemy' role but kinda one dimensional.
With the BW onwards dynamic they have the potential to be more humanised, if still vindictive enough that you can still root for the trio getting the last laugh. The trio are still incompetent, but they're getting praise and special perks they have to put genuine work in for. OF COURSE they would hate their guts. It would also make Giovanni's retooled dynamic with the trio stand out more, with someone desperately trying to clue him in. Even if they didn't bring back an old Rocket member, they could make a new one with a similar background.
We actually don't really look into that area much, characters who work their ass off only to get upstaged by someone who gets by on dumb luck. I mean it happens a LOT in the anime due to excess plot armour, but it's rarely an intentional plot device and there's seldom resentment about it in-universe, the show rarely has that cynical tint anymore. Plus I love comedic works where the evil organisation is treated like just some jaded workforce (it's one of the reasons I think Robot Chicken Star Wars is more compelling than the real deal).