You're not wrong, but I think a lot of that comes down to public profile and the weight of history more than any reasoning in-story. Lots of heroes are just as powerful, if not more so, than the core 7. Firestorm, Zatanna, Fate, etc etc, can go toe-to-toe with Clark and J'onn and Diana and Hal. But the big names are the Big Names, and they're the ones we're always going to associate with the team.

Everyone else....they can be viable, valuable members but no matter how awesome and useful they are, they're going to be the new/secondary faces.

But hey, once upon a time Zee and Hawkman were new faces to the League, and these days they're almost always mentioned in "who should be on the team?" discussions. They're not the Big 7 but they're still seen as important Leaguers. Vic, Jeff and the rest could be seen the same way with a little time and effort.