Every single person arguing for a 5e warlord on these forums has explicitly expressed their willingness to compromise, and have acknowledged, usually without being prompted, that no class is going to port directly from one edition to another.
You can never say 'every single one' but, yeah, really close.
And, profound compromises have already been made (maybe not willingly, but they happened, and we're not edition warring & burning books, are we?). The exclusion of the Warlord from the PH was a huge compromise, it's not part of the standard game, only those DMs who opt into it will see it impact their campaigns. On the other side, there are little mechanics here and there that might be representative of individual things a hypothetical Warlord might someday do, they add up to letting go of most of the more specific quasi-mechanical objections.
It just remains to go the rest of the way, and finally have the option of an official Warlord enter development.
Literally every single claim you make about other posters in this post is factually incorrect. Every. Last. One.
So in the end, I'm not even really sure who you think you're conversing with.
Could all just be one of those edition-war flashbacks. I get those sometimes. Very unpleasant.
I end up going back and editing a lot of posts.
I'm arguing 2 linked, but separate things.
1: at-will support can be done. No mechanical reason why it couldn't be balanced. (Except healing, though at-will healing that reduced max HP could work). (Though there are still ways to limit something without doing x/day. Like "at the start of each battle", or "when you kill an enemy" or "you can only fool an enemy once", etc...) This applies equally to cantrips, invocations, or martial maneuvers.
OK, I'm seeing something, there. If an ability is at-will, in that the character can use it every round, all day, if he wanted to - you could stand there giving inspiring speeches to the daisies - but they have conditional requirements, then they're not really at-will. Similarly, they could consume other resources (HD are the stand-out candidate, obviously) in the process of enhancing them, then the ability is at-will, but the linkage to the game's attrition model and resource mechanics remains. The problem with that is that existing support characters bring resources, themselves. That could be tricky to get right... the boost given to the expended resources would have to be substantial.
2: it would fit the narritive. Getting in and supporting round by round, and not suddenly stopping and being unable to do it.
Meh. Abstraction is a legitimate thing in D&D, always has been. Any given tactical trick, combat maneuver, inspiring soliloquy or whatever is going to have moments when it'll work, and moments when it won't - be irrelevant the vast majority of the day spent out of combat. That could be modeled in extreme detail, or it could be abstracted all the way down to n/rest. Either extreme is legitimate and there's a fair universe of design space between. (And I'm glad we have professionals to sort it all out.)
2b: we have enough x/day based support classes (possibly including the mystic). Something different would be nice.
Being adequate support from a non-supernatural source was revolutionary enough - revolutionary enough to be sent to a gulag in 2010 and still be trying to get a meeting with your lawyer 7 years later. But, yes, while we're talking things that might be nice, sure. And, that overt mechanical distinctiveness, problematic as it might be in this case, is very much in keeping with 5e's class design philosophy, as evinced in the designs we've seen, IMHO.