Eh, they're all over the place in 5e now, so why fight that fight here, it seems to be a ship that has largely sailed. Battlemaster in particular has tons of it. Now maybe it chafes some people, but it has the virtue that the player can sit down at the table and understand what he can and can't do without the need to parse nebulous requirements that he may suddenly find rule out things that normally you'd imagine would work.
Sure, 'nebulous requirements' aren't the best design, but, they can be evocative. And while 5e has plenty of x/time limitations, nothing requires any given new class or mechanic to cleave to that. It's messy and old-west-shoot-from-the-hip, but it leaves possibilities wide open that more disciplined design would close off.
And, 5e places it's faith in the Empowered DM to keep it from all boiling over. So no reason at all not to explore something different with the Warlord (or psion, or warden, or shaman, or anything else that might be down the line). It might not balance well, it might run into problems situationally, it might bring a round to a screeching halt, but a DM who can handle what 5e is already throwing at him, can handle that without breaking stride.
It's actually kinda exciting, in a way.
I think these are complicated mechanics that add a lot of extra die rolls and book-keeping at a very low return rate.
I definitely agree about bookkeeping, that can be a drag, any bookkeeping-heavy approach to a neat new rule or sub-system should be side-barred, even if the whole thing is already optional, just to emphasize the potential fun-sucking-vortex of boredom.

But, for those to whom the extra soupcons of realism or consistency or whatever is worth it, it'd be cool.
This is probably why in ALL editions of D&D this sort of mechanic has AFAIK never really been used (maybe I've missed some obscure nook of the game somewhere, but I know of no PHB class in any edition that ever had such a mechanic, and MOST of them have had at least one "one time per ..." kind of mechanism.
I can't call one immediately to mind. I have a vague sense of more obscure stuff, magic item creation, maybe, or something to do with henchmen... or,... no, it's gone.
And, you're right, a novel mechanic can be a bit of work for little return. That doesn't stop us from having multiple methods of spell casting, or three fighter builds that all work differently (noth'n vs CS Dice + Maneuvers vs Spell-casting), or Ki-zapping Monks, and I'm actually half-hopeful it won't stop much else, either.
The Standard Game can stand as a bastion against bloat, while the Advanced Game gets all experimental.
As I always told people when they had issues with something like this in 4e, narrative always trumps rules. Whenever we explained some limitation in a narrative way, then we followed the narrative logic when something of real consequence hung on it or where the narrative took place outside of the specific context where the mechanic was really relevant
I suspect that'd go over even more easily in 5e, yes.