You know it sounds reasonable, "Why not just let people have Warlords if they want them?" But adding things to the game changes the game for everyone, not just those that play with the new addition.
That's just not true. If you don't use something, it has no effect on you.
Now, it may be that things snowball going forward. That a new class introduces new mechanics that are so useful they get re-cycled for new sub-classes of existing classes or for monster write-ups or whatever. But you can hold the line against that. Either by cutting more and more of new material as it comes out (which might, eventually, become a little onerous, but is still much easier than creating new material yourself), or by freezing the game at a point in time, if new material becomes too pervasively
If you add psionics to the game, now you have a world with psionics in the world. So you lose players that don't want to play in that type of game. You can mitigate that some by making psionics "optional", but you will still lose people. There are other games out there, maybe games that might appeal to that player more.
By that theory a game can only broaden it's appeal by having less. The ideal game would have nothing. That's nonsense. 5e provides many options, conveniently grouped in the free basic version of the game, the 'Standard' version, and whatever combination of opt-into and out-of optional rules & modules a particular DM wants (one example of that being whatever is AL legal atm). Those options make the game more inclusive, not less.
Until you have psionics, players who want that are being excluded. Once you add it, they're included, and people who don't want psionics simply don't use them, and remain included.
Like it or hate it, D&D 4e split the community. Not saying that adding a Warlord will have the same effect, but the farther you go towards 4e, the greater the chance of a schism.
Bringing the community back together was part of the mandate of 5e. That means 5e needs to include fans of 4e as well. Positive inclusion means accepting that the game will include things others like, and that you don't, but don't have to use and can safely ignore. It's not much of a burden to take up. For the most folks, it's a lighter burden than carrying around a lot of resentment towards others.
But the pro-Warlord groups want Warlords in the default setting. They want Warlords in Forgotten Realms and they want them in the Adventurer's League. And Wizards of the Coast is free to do that.
Personally, I could care less if Warlords are in Forgotten Realms, since I don't particularly care for playing in that setting to begin with. But, sure, the concept is as valid even in magocentric FR as in any fantasy setting and there'd be little reason for the setting to ban them - though nothing would force a player to use one nor keep a DM from banning the class at his table. AL, as with all new material, can probably be expected to allow the Warlord for a season or so when it's first introduced, and that's it.
The question is will adding an official Warlord increase or reduce the total number of 5e players?
It can only increase the number of 5e players. By how much depends on how well-done the class is. The more successful it is in expanding the range of character concepts available and playstyles supported, the more players it'll attract.
If adding the Warlord will add more players than it will drive away, then they should add it. If it will drive away more than it will add then they shouldn't.
That kind of cynical calculation is antithetical to the inclusive spirit of 5e.
No one should be driven away by the inclusion of an option. If it weren't optional, if you were, indeed, forced to play a class you didn't like or if it were inextricably woven into every setting, sure, it might 'drive away' some people. But that's not the case of /any/ class and wouldn't be the case with the Warlord.