If you go back to the original definition of hit points as including factors beyond physicality, such as stamina, luck, morale, and divine favor, enchantment makes a little sense as being able to heal hit point damage. However that's not something WotC has done before; even with 5e Heroism, that spell grants temporary hit points, not actual hit point healing.
I'm not convinced that "putting healing spells in the right school" is less important than "putting all power words in the right school", if you want your design to be elegant. It should be noted however, that since their introduction, which spells go into what school is constantly shifting. In 2e, for example, Alteration was huge, as a lot of spells were felt to belong in the "change thing to other thing" category, but even then, there were simply spells that didn't belong (Burning Hands, Color Spray). 3e corrected this, though their real purpose was to make the schools more balanced against one another (Burning Hands became Evocation, Color Spray became Illusion).
5e however, has no real reason to balance schools against one another; most classes simply could care less what school a spell belongs to! And ironically, the subclass that would care about Enchantment the most, only has two benefits with regards to Enchantment spells, making them cheaper to scribe, and giving a single target Enchantment a second target (which wouldn't even affect PW:H even if they somehow got the spell!).
This really strikes me as really making evident the fact that what school a spell resides in really doesn't matter very much, and is an artifact of older game design, like alignment, that has become vestigial, with very little actual use, and only persists because it's one of those elements that makes the game "feel" like D&D. Arguing about Necromancy vs. Conjuration vs. Abjuration for healing magic is academic; if a spell doesn't feel like it belongs to a given school, the DM can simply change it with very little impact on the game.
In fact, I think Wizards should stop worrying about this themselves, because all that's going to happen is, someday they'll give someone an ability to do something with a blanket school of spells and a player will find a spell that was never meant to be used with said ability and, well, use it, which will only force them to say "oh this is a mistake" in some developer tweet, which most DM's will never find out about until they visit a forum or something, lol.
Also, they are definitely going to shoot themselves in the foot over things like this; I highly doubt they're going to update all of the old 5e spells to this new paradigm, but "backwards compatibility" will mean someone is going to find a spell in an old supplement that doesn't match the new paradigm and do something ridiculous with it, lol.
