So from what I gather is that people don't want the warlord because non martial HP healing is dumb and shouldn't work like magic. Ok ok of course this is an incredible over simplification and I acknowledge that. This topic isnt really about the warlord, but about why people want or don't want something in the game.
People want the Warlord because it was a great class, that gave solid mechanical support to concepts and play styles that couldn't be done well before (and, in 5e, once again cannot be done that well at all).
People don't want the Warlord for the reciprocal of the same reason: it opens up character concepts and play styles that they don't approve of, and do not want to allow anyone to play.
You can ascribe all sorts of motivations to those desires - many of them having to do with the edition war, including the edition-war skirmishes over how to over-analyze hps that you allude to, or 'caster-supremacy' agendas (or the reverse), or whatever - but the basic issue is that the Warlord expanded the character concepts you could play in D&D and the styles in which the game could be played.
The question is this... I don't get the idea of being opposed to something that many people clearly want. People limit things like races and magic items and things like that. So why can't people just disallow the classes? Think martial healing is terrible and shouldn't be a thing? Don't use it. It's literally that simple.
It is, but doing so makes you theoretically 'wrong' on some academic 'RAW' level. That seemed really important under the 3.5 zietgeist, but it really shouldn't matter in 5e. 5e is meant to be a unifying edition, for all prior fans of D&D (and incidentally, it's hoped for potential new ones), and that mean no one gets to be 'right,' even though, inevitably, the default Basic and Standard games have let certain fans feel that way (arguably old-school Basic and AD&D respectively) a bit more than others.
It seems childish to not want something but then force your opinion and views on other groups who have completely different expectations and playstyles. Can someone clue me into this kind of mentality? Is there something I'm just overlooking? Does the game actually force you to play these classes, was it a rule I overlooked or something?
The idea is you can invert that argument. By including a class, you allow a sole player at the table to 'force' everyone to play a certain way just by picking that class. That's both absurd on the face of it, and a meaningless truism. It's absurd because players should have some basic respect for eachother, for the DM's vision of the campaign, and should communicate enough to know what kind of campaign is being played. It's a truism because any/every class implies things about the setting and the nature & tone of the campaign, and can affect how PC's interact & players get along.