Priest has been pigeonholed into a lesser version of all the things that it's "supposed" to do well. I imagine it has something to do with player complaints about how "unfun" the class is to play against.

Because you know, it has that reputation of being the class that steals your cards, although Rogue excels at that much more at this point. It has that "blue" reputation where it supposedly cancels out your gameplan in an unfun way, although Mage excels at that much more at this point. It has that reputation of being the "control police" that supposedly outvalues all other control decks. Every single control deck excels more at that at this point.

People don't seem to care whenever you offer those aspects to other classes, but suddenly it's "unfun" when Priest is allowed to actually excel at what it's supposed purpose is.

I really don't even know what's left for Priest as far as something it does particularly well. Heal? Except we've moved past a value oriented meta a very long time ago, so you can't even bother with stuffing too much healing in a Priest deck if you want any chance of winning. Warrior easily obtains much more armor than a Priest can hope to heal anyways. So do certain fucking Druid decks nowadays.

I don't know. Baby steps have been made to make Priest vaguely better than dumpster-tier the past couple of expansions. But it needs a lot more. It needs to be allowed to do what it's supposed to be good at. It never is. Until that point every matchup will be like what you described, where another class simply out-Priests Priest.