I guess I don't understand what a Warlord is. (I'm not being snarky, I've never played one and it's not in any of the books I own.) From what I've gathered from the forums here, it has a lot in common with the psion: it's not a "magic user" in the traditional sense but it has magic-adjacent abilities, nobody can agree on what it is supposed to look like, and Wizards of the Coast hasn't gotten it right yet in 5th Edition.
For me, at least, the Warlord
emphatically is not magical.
It is, without a doubt, at least a little fantastical--because everything in D&D is fantastical. We have Fighters who can--once, until they take an hour nap--decide to attack twice as many times or shrug off injuries. That's clearly not completely mundane, but Action Surge and Second Wind aren't supposed to be
magical.
The Warlord is several things. From a Doylist perspective, it is a "full Cleric replacement" (able to cover all the important functions a Cleric could cover in 4e: healing, granting attacks, permitting saves against save-ends effects, buffing allies, debuffing enemies, etc.), a decently-armored and usually melee combatant, and a Martial character and support that's supposed to be exciting to play
as support. From a Watsonian perspective, it can inspire or coordinate allies to do their best, to draw on the resources they might not be able to draw on normally; it's a force-multiplier, whether by taking great risks, deploying clever plans, or carefully using resources; and it's a tactician and analyst.
Part of the reason I think you've seen such disagreement is because there are two very vocal camps. You have one camp, which I'm in, which wants a 5e Warlord to be as close as it can be to what the 4e Warlord was, just translated into 5e mechanics. On the opposite side, you have a camp that wants the 5e Warlord to be very little, if anything, like what the 4e Warlord was, and instead trying to fill the concept with totally new mechanics unrelated to the old ones, seeing this as a workable compromise between the "we want our Warlord back" camp and the "there should never, ever be a Warlord in 5e, period" camp (which isn't directly relevant to questions about what the Warlord
should be, since they don't want one in the first place.)
As you can probably tell, I find the second "let's make a 5e Warlord that doesn't actually do the kinds of things 4e Warlords could do" camp extremely frustrating. One of their common requests, for example, is that any Warlord should not provide ANY healing whatsoever, and should exclusively work in THP. This is a pretty major sticking point for anyone wanting a reasonably-close 5e translation of 4e mechanics, because
it's not a Warlord if it can't actually heal.