Are you familiar with the word you used, "conflated"? Anyways...
THPs don't fit because inspirational healing is the thematic equivalent of the clip I posted above (reposted here, because who doesn't love Burgess Meredith). If the healing is THPs it creates an incentive to use it to "get it up" before combat over using it to rally an ally who is hurting, and that goes against the very fiction that inspirational healing aims to emulate. An ability that grants THPs will almost always be used by cautious PCs before battle begins, and that changes the very nature of the ability from healing to buffing.
I disagree. THPs last until they are expended, or a long rest is taken. So no. If, late in a battle, someone is badly wounded and receives this benefit, those THPs will help the now and/or carry through to the next battle. They are functionally the same as any other HP on the PC. The wounded character is still benefiting from them no differently than if it was a cleric healing them. They are farther from 0.
In fact, if anything, using THPs are fundamentally
better at emulating inspiration for two big reasons:
1) The inspired individual can also receive actual healing, thus allowing the inspiration to carry through even if they are otherwise healed (or managing to go unscathed in the fight). With healing, the inspiration effectively wears off once the cleric restores them to health. Why did they lose their motivation when the cleric chanted over them? That makes no sense.
2) And because THPs can be used effectively either before
or after a battle, as I explained above. If the ability is just plain healing, they are useless in advance of the fight and cannot emulate the
much more common trope of pre-battle inspirational speeches.
Therefore, healing is the wrong method going forward. THPs are the only right way to go, IMO. They are much more flexible while still serving the same benefit.