Aid increases the maximum hit points of the target.
I don't recall a single cleric spell that grants thp. Bards have one with heroism and there's false life for wizards. But not many.
Enhance ability: Bear's Endurance. Advantage on Con saves, 2d6 THP which are lost when the spell ends (concentration up to 1 hour).
Other than the one stated above,
Heroism,
armor of Agathys, and
false life are the only spell-based sources of THP. Fiend Warlocks also get Dark One's Blessing, Battlemasters get Rally, and Inspiring Leader grants some. Otherwise, THP are, I am somewhat surprised to admit, relatively thin on the ground from what I can tell; I really only skimmed through the Cleric list for THP spells, so I might be missing something from a different class.
Though the simple fact of "a meaningful number of THP granted would make the Inspiring Leader feat a
notably subpar choice" (thank you,
censorship chat filter...) certainly doesn't help.
Which is true if that character does not get hit for the rest of the adventuring day, as the thp stick around. Unless you're giving thp to the bow ranger or wizard it's a safe bet people will be hit.
You can also choose to heal the wrong person too; a couple injured PCs, heal one, and the other gets hit and goes down.
It's not a strong complaint.
As long as the THP do in fact stick around, sure. Though I gotta say, simply shouting "THP are the answer!" leaves me a little cold for a big, big reason (which I still have yet to see a response to): How is it gonna be balanced, especially at the lowest levels? You've made it abundantly clear that you think an HP-based ability would irrevocably destroy a 5e-Warlord's access to Warlord-y features. As I've said elsewhere, if we're actually going to avert the "one-or-more people unconscious for 1d4 hours" problem, we're gonna need some serious THP--serious enough to (
at least) double a first-level PC's pool of hit points, possibly even triple for the squishiest classes (who can, quite easily, go from full to 0 in a single hit--a Con 12 Wizard has only 7 HP). Simply throwing out 1d6 THP to a single target ain't gonna cut it. A lucky damage roll from many CR 1/2, and even some CR 1/4, creatures can do it--a Crocodile can even take down a Fighter with a +2 Con mod on a max-damage roll (which should, in theory, happen 10% of the time...)
And if you do hand out enough THP to make the difference, what's keeping this thing from being ridiculously, game-warpingly OP? That's the dark side of your arguments about their power, after all. If they're just as good as HP, as you claim, yet they can be handed out frequently and to all party members (which they'd need to be, to prevent the aformentioned "1d4 hours unconscious after most every fight" problem), it's starting to sound like your THP-based Warlord would make the first few levels a
cakewalk...and then risks becoming obsolete thereafter when damage out-scales it.