Is it important to WotC to develop classes that will see actual use? If so, how does that goal weigh against the goal to get 4e warlord fans on the 5e boat?
It doesn't weigh /against/ it, the two are in perfect accord. A good 5e version of the Warlord /will/ help combat the appearance that 5e is actively excluding 4e fans, bringing more of them back to the game, /and/ it will see use by those fans, by existing 4e fans already playing the game, and by new fans, and by other current fans who haven't been unalterably prejudiced against it by the edition wars.
The other important point is that the class should be designed for those fans who will, in fact, use it. Not to somehow appease those who won't.
Is that a good use of development dollars/page count/the current 5e fans it will irk? Exactly how niche are we willing to make this class? What if someone is in that niche but is at a table of people who aren't?
You don't know that it's all that 'niche' - there is a real danger that a well-done Warlord could bring people currently opposed to it around. In any case, as in any table that has mixed opinions about something, mutual respect will have to prevail - something that's apparently much easier in person than on-line.
Is a narrative that might be magical something that eradicates more objections, so that the class sees broader use? Is that worth turning off some of the more hardcore 4e fans and some of the more hardcore warlord haters?
There are 5 or 6 magical support classes already, there are non-magical support classes, and one extremely poor support archetype that's non-magical. There is no need for another magical support class. There is a need for the non-magical Warlord.
You can, of course, decide that it's not actually that worthwhile of a goal and say, "don't like it? BAN IT." I don't know if WotC would follow suit on that or not. I suspect not, but it's not something anyone has real data on except maybe WotC themselves.
Every extant game element that doesn't have a specific alternative module in the DMG is already in the category of "don't like it, ban it.'
The entire idea of a "not-necessarily-magical" compromise is predicated on the idea that a more broadly acceptable class is a worthwhile goal that is not necessarily impossible.
The concept of the warlord, and it's past implementations have all been magical. It would be starkly contrary the 5e's design philosphies to do a 180 from that. The disadvantage of a very ambigous presentation is that it undermines the concept of the class and breaks with it's past appearances, effectively destroying it. You lose fans who actually want the class, in the hopes of bringing in a few who specifically want a magical warlord.
But it seems implausible that anyone really wants to play a magical Warlord - they'd just play a Valor Bard.
OTHO, a compromise that wouldn't sabotage the concept, but still allow anyone genuinely troubled only by a few features functioning 'mundanely' would be to stay true the class, but offer an alternate interpretation: A side bar that opens the door to some characters /believing/ that the Warlord's abilities are magical would be a 'compromise' that wouldn't unduly damage the class, but removes the objections that it's abilities are too much for a 'mundane' character.
Something like:
Sidebar: Some attribute the extraordinary abilities of famous Warlords to a divine heritage or blessing, or some supernatural connection to primal forces of conflict, or even simply to luck or fate. Some say that there must be more than just charisma or brilliance behind a Warlord's string of improbable victories. Most Warlords would agree, there is something greater than them that deserves the credit for those victories: their allies.
How is this different from a nominally neutral 'maybe warlords or magical or maybe not: you decide?' Well, for one thing, it still supports the class concept. For another, it has complete deniability. If one player decides his Warlord is the son of the God of War, and another says he's just like anyone else, there's no way for one to 'prove' he's right. OTOH, if with the maybe-magical language, the DM is essentially encouraged to rule one way or another, and change the mechanics to suit, undercutting the class concept.
Leaving open /beliefs/ about the class, means two players with different opinions about the class /can/ play at the same table, without necessarily wrecking the game for eachother. (Really, they should just have the mutual respect to do so without needing a side-bar in the class description, but, hey, if it helps, it's probably less than a column-inch, well worth it.) Presenting them with a binary option invites repeating the arguments we have here at the table, and, once the decision is made (probably a DM ruling), leaves one of them disappointed.