I'll just point out that you pretty much dismissed the first viewpoint by describing how it relates to somebody being "impossibly" tough, so I imagine those on that side of the debate would take a bit of offense.
They might, but it would be unjustified. All-meat is an extreme concept of hps, back in the day, it was only expressed in the sense of mocking D&D for being so 'un-realistic,' no one used it without resorting to some supernatural rationalization, like pools of life force on the positive material plane (no really), or leveling up making your flesh denser until, at high level, you were practically a Marvel-Comics Asgardian.
You could have at least balanced it by describing some of the paradoxes introduced by martial healing of non-meat HP.
Those can be contrived fairly easily, you just have to read more into the hp system than is actually there, and ignore some of the contrary implications. For instance, if you assume that being dropped to 0 /must/ indicate a mortal wound that can only be healed with medical treatment and time or waved away by magic, you can get the restoration of hps without literally healing the wound to look a little odd. However, to make that assumption, you must ignore death saves, which allow a character to get back up after being 'mortally wounded,' and act normally, unimpaired by the wound, and to re-gain all those lost hps from that mortal wound after a mere 1hr rest, or, at worst, a night's sleep. If you don't ignore those bits of 5e, then either wounds heal with supernatural rapidity in D&D, or 'non meat' hp restoration can restore all the hps lost to wounds.
But beyond that, it's only one facet of the Warlord dispute. I only ever see a few people bringing that debate into it.
It's really the biggest one. It started during the edition war to attack overnight healing, healing surges, and Second Wind - and thus 4e in general. It's still being used to attack the Warlord, even though HD, functionally similar to surges, and overnight healing are already pat of the game.
Yet I truly loathe the Warlord concept.
El Mahdi (above) expresses the core of the reason I detest the concept, far more eloquently than I have managed. Ironically, I think his intent was to defend it.
Yeah, he put literal 'Leadership' right at the top and harped on it. Warlords can lead other PCs in a litteral sense, in combat, it's one way of narrating their abilities, though not the only one. But, like all "Leader" Role classes in 4e, they were not automatically party leaders, just because of the name of their formal Role in contributing to the party - which was a support role, including managing hps, buffing, and the like.
I'm surprised you're still stuck on that misinterpretation, though. I thought we covered it well enough in prior threads, including going over a whole range of non-party-leader warlord concepts.
Or, did you move on from that to the whole objection to PC abilities affecting the 'emotional states' of other PCs. Because, I thought we pretty thoroughly addressed that one, too. For instance, that such abilities generally contained language that they only affected allies, and could in essence, be declined by the ally, if desired by simply not availing themselves of the effect. So there's no 'loss of agency' because a Warlord tried to 'inspire' your character - if you decided he's not inspired, your decision stands.
Of course, your character may not stand very long without those benefits, but, as whenever a PC RPs a trait or flaw in a way that's detrimental to him, the DM might well - and ironically - award you Inspiration for good RP.
So, I'm surprised you're still stuck 'detesting' the concept, rather than being concerned about the implementation.