A new hope will emerge

I agree it's time we saw Jedi who target other factions the way other characters are specifically Jedi killers.

This.

I seem to remember an obscure quote about Jedi specializing or some such. Probably no one else remembers it, of course, or the game designers would have given Jedi some ability to specialize under specific leaders to beat specific factions.

Again, pretty obscure, but I think it went something like,

Chancellor Palpatine, Sith lords are our speciality.

Maybe it's just that the Devs have never heard that quote before.