Some HP types, if they overlap in effectiveness with charge moves, could be goot for some match ups. I dont know how HP psychic compares with extrasensory, but HP psy mich be good against pokemon like machamp when paired with brave bird, or for poison type grass and bug types when paired with fireblast. Presently, Ho-oh's a very tanky pokemon, and while its stats are absolutely fantastic, its charge moves are...less than, though that is due to main series limited movepools and niantic giving it not the best moves it can get. It can get overheat and sky attack, but instead niantic gave it bravebird and fireblast (though fireblast isnt a terrible move, its just not as good as overheat)
HP Ice, water, grass could be good as a tanky groudon counter when paired with solar beam for PvP, and possible poison, or bug with fireblast against non-poison type grass types in raids/gyms, but those seem scarce.
The problem Ho-oh has is even if it does get a benefitial STAB HP, its charge moves arent the best. Realistically, I can see niantic doing a kind of ho-oh raid day in the future, either adding will-o-wisp as a fast move or making all ho-oh on the day get HP fire If they do a sacred fire raid day, or HP flying if they give it a better flying charge move like sky attack or add something like skydrop or fly