Face priest has a lot of the tools face hunter has to win the game sans hero power (and I've seen people play shadowform in those decks to counter that), plus the advantage that nobody mulligans around that shit (probably the reason it wins most of its games tbh, so pretty gimmicky at best), and a few better cards in similar slots. We're creeping up on enough cards that just do efficient damage that it's not entirely unrealistic. But no, that deck won't ever influence anything cause it's not all that different from face hunter, so it'll just rise and fall with it at best, and that style of play isn't even all that popular at the moment. It's just another fast deck is all, but at least it has a plan and sticks to it. I wouldn't call it illegitimate in the slightest.
I love tempo style priest builds, but I'm still unsure about dragon decks. They're definitely not easy to play, especially the priest version, and I don't think they're bad either, but it's just not my style. Feels like reverse mech mage or undertaker decks when those existed, in that the restrictions on your curve require drawing top end earlier instead of mulliganing for it, and I didn't even enjoy having to mulligan for my synergy. I haven't done the math on how many dragons of each mana slot affects things, so my opinion might change, but the starting hand size of this game is probably too small imo. I guess my problem is a lack of motivation, like why include all of this synergy when its so hard to pull off and I could just play a different priest list to tech around the meta.