The only reason it didn't was because I wasn't trying to envision what was happening in-fiction at all. The problem, in that case, was with me not paying attention to the fiction.
That's not a problem, at all. Do you normally envision the 'fiction' corresponding to absolutely everything every character does? Do you analyze it's implications at the table? No, clearly you weren't. It's only when you go intentionally looking for a problem that you create it. The point of the game is to have fun, not to go digging for imaginary problem and blowing them out of proportion when you can just let your imagination go in directions that /are/ fun, instead, or, worst case, skip over the boring/annoying bits...
I haven't heard a solid alternative so far, just a lot of "It doesn't have to be like that, but your table can figure out for themselves what it actually is."
Offered quite early on:
Good tactics could indirectly result in better morale, if you see a tactic succeed it could buoy your resolve, if you have seen tactics pull victory from the jaws of defeat before you could be less inclined to give up. It would be a case of the character not being inspiring so much as the events the character set in motion. Inspiration needn't be a rousing speech (which your average RPG nerd might not be too likely to deliver convincingly, and another such might, perhaps one on the cynical side, be all too inclined to imagine as hackneyed), it needn't even be positive. You could be inspired to do better by words, or, perhaps by deeds, or even by wanting to show up a rival. That one PC inspires another, giving him a bonus, needn't mean the inspired PC looks up to or respects the inspiring one. In genre, heroes may get inspired by other heroes, they can also be inspired by a plucky side-kick, despised ally of necessity, or bitter rival. The nature of the relationship would inform the narrative, and may or may not have a bearing on the resolution of the mechanics.
It's actually a topic that's been covered earlier, too (for that matter, much earlier, all the way back to the 4e PH1 and the discussion of the 'Leader' role, that it doesn't imply authority nor making decisions for everyone else). More recently, though, in this temporary forum, we've gone into the range of concepts the warlord might enable. The plucky side-kick, the faithful retainer always ready with good advice, the pragmatic tactician, the instigator who goes off half-cocked, the manipulator, the bitter rival you feel driven to out-do at every turn, even the perennial victim inspiring heroes to come to the rescue.
I don't know how much detail or how many examples it'd take for you to acknowledge there are 'solid' alternatives to the Zap Brannigan stereotype the naysayers have manufactured, but I'm willing to give it a few walls of text if that's what you need.
The goal of being inclusive is admirable, but it will not be 100% achievable. There are going to be parts of 4e that people like and want in 5e that other people don't like and don't want in 5e. So what do you do? You can't please both groups.
You can include both groups by including the desirable-to-some material outside the Standard Game, and letting those who don't want it ignore it. For instance, feats are a 3.x-ism that not every old-school D&Der is down with. They're also officially optional, the DM has to opt into them, and, even if he does, if you don't like feats, you can take all your ASIs as stat bumps.
4e has a certain feel to the game. The Warlord embodies that feeling. 5e has a different feeling that, while not completely incompatible, is different by default. It's my opinion that the Warlord should be an option that must be explicitly added.
At this point, that's all it /can/ be. The Standard Game is defined by the PH and set in stone. Like SCAG's Bladesinger and PDK, any forthcoming Warlord would be very much optional material, probably see the light of AL at most once in whatever season coincided with the product it appeared in.
Classes, though, like any player option, are, well, optional by nature. Even if the Warlord were in the PH1, no one at a given table is forced to play one. It's not like 1e when you 'needed a Cleric.' A group would have to have something more against the Cleric, Druid, Bard, and Paladin before they'd even begin to feel pressured into 'needing' a Warlord.
'Optional' is a given.
