If the Warlord had ever "shouted arms back on," then 'Warlord Healing,' wouldn't be an oxymoron, and the mechanics of it would have been nonsensical (perhaps still perfectly OK, mechanically, but as nonsensical as any other fantastical element when judged by standards of sober realism).
But that was never the case: It was just edition war rhetoric.
5e's style of presentation and prioritization of DM empowerment lets you exclude things you don't like about the Standard Game. When it comes to excluding optional elements (which any version of the Warlord introduced at this late date would be), it's a trivially easy matter of not opting in.
Bad mechanics do. A bad mechanic is not a matter of opinion, though, it's one that's actually problematic - broken, incoherent, imbalanced, unclear, or just plain not playable as written. But just because you don't like a concept a mechanic models or the way it models it doesn't make it bad.
And, there are mechanics that only become bad if you muck about with the assumptions upon which their based. In the example of making something like Inspiring Word literally 'healing,' for instance, by changing the meaning of hit points from the slightly unintuitive, abstract mix of factors first articulated (exhaustively) in the 1e AD&D DMG, to a nonsensical-in-it's-own-right all-meat variation. For another instance, changing the assumed day-length from an attrition-based 6-8 encounters to typically only 1 per day, renders daily resources imbalanced and a 'bad' mechanic. In neither case is it really the mechanic that's bad, though, they're each fine within their context, it's just that changing the context requires changing the mechanic in some way to fit it better.
To illustrate with both the above examples:
If you decide to institute all-meat hps in a game with some sort inspirational or other non-magical 'instant' hp-restoration, you could change that mechanic to restore hps only until the next rest or until the end of the encounter, instead (not healing, but not max-hp-exceeding temps, either, but something slightly inferior to both - and compensating them for the reduced effectiveness in some other way, like more hps restored or more frequent use).
If you decide to run 1-encounter days consistently, you could salvage and re-balance daily resources by making them 1/6th or so as available and/or making short-rest resources as powerful as long-rest ones (essentially there's no difference in availability between the two in such a campaign).
That's a matter of your personal opinion and how you want to play the game, and it would be trivially easy for you to opt-out of any such optional material.
A personal feeling of alienation could be brought on by anything. A change in a perceived pattern of game design, an improvement in game balance that leaves a favored class less-unfairly advantaged, a different style of art, a smaller book format, a new font - anything.
It's an irrational, very human, unpredictable thing.
When it comes to optional material, I have to disagree. Don't like a new thing, don't opt into it. Simple. The alternative is nothing more or less than dictating to others how they play the game.
Now, when it comes to the Standard Game, yes, material should be as balanced, inoffensive, and greatest-common-denominator* as possible. And, no, no game's perfect at that, either.
Edit: * trying to avoid the negative connotation of 'least common denominator' while still getting across the idea of maximizing breadth of appeal by limiting content.