From the perspective of that HR process, they generally care about the employee as much (or as little) as about that manager. A manager may start some process, but HR might as well consider that it's better (or easier?) for the organization to replace that manager instead of replacing that individual contributor.
I'm not sure I've ever heard a story where a manager attempts to fire someone, but HR decides to replace the manager instead. Is that something you've seen? I only hear stories about managers being protected as hard as possible by HR.
Yes, I have seen unit-level "personality conflict" situations being resolved by firing the line manager.
It's important to note the distinction between "manager" and "management". In larger organizations an entry-level worker is x levels away from top management, and a first level line manager is x-1 levels away from top management, where x is 5-10 i.e. they are quite far from management and very close to the actual worker.
In a large company, from the perspective of actual decision makers or HR, a first level line manager or a team lead is just a slightly different job description of anonymous interchangeable peon. You have a hundred customer service representatives and a bunch of CS teamleads; you have fifty small branch offices/stores/warehouses/whatever and so you have fifty mostly interchangeable branch managers. Their role is supervising the team and executing the assigned goals and policy with minimal influence on it - any actual policy is set by that manager's boss boss or higher; any policy exceptions are likely to require approval from that manager's boss or higher, etc. Of course, if you have only a hundred or so people in the whole organization, then it's different, and most organizations are small or medium enterprises - but quite a few people do work in large corporations.
I've seen it only once. One manager, not in my department, had a high turnover. Staff were either fired, quit, or transfered. Senior management eventually stepped in and discovered this guy was pretty toxic. But they couldn't simply fire him. Since he was well-connected in the industry they gave him time to find another senior position.
In any remotely sane company, HR does what management says. The manager may well be replaced, but it's the manager's manager or someone even higher in the food chain who makes that call, not HR on their own.
They way I've seen it, the manager's manager formally makes the call, but they wouldn't really know the other person involved (they would just work with their subordinate managers) nor the details of the particular problem. If they care, then they would get into the details and perhaps fire whichever of the two is actually at fault; but if they don't care much (which I've seen happen, especially in more lower paid/mass market positions), they would rubberstamp whatever HR says - especially since it's not that unlikely that the conflict will escalate into a complaint (no matter if real or not) about discrimination or workplace abuse, and so from the perspective of that manager's manager it's very important that a Proper Process gets followed and (for many jobs, though usually not for IT jobs) not that important to them about who stays and who leaves afterwards, as HR will just get an equivalent replacement.
HR has their own obligations to the people they report to. If they can't justify the manager's suggestion without sticking their necks out to a degree they're comfortable with they probably won't.
They'll mostly side with the manager (because selection bias, not a lot of managers are bringing them cases of people they want fired where that outcome is not compatible with the processes) but may very well tell a manager to just deal with it if that's what's "doing their jobs" looks like.
Things like this are never as black and white as people looking for cheap upvotes make them out to be.
I don't think we're disagreeing here? Of course HR can and will push back if (say) firing somebody without proper CYA could result in a lawsuit, but the point is that HR is not the one initiating any firing -- that has to come from management.
In general, in larger organizations with formal processes, HR would look into the situation instead of simply accepting the manager's assertion about someone being a bad performer.
For example, it may be quite clear even from externally looking at other reports (e.g. data from "360-degree reviews" or whatever internal evaluation process the corporation uses) that the consensus around the team is that the person is not a bad performer, but that the team lead has had recorded "problems with cooperation" - in that case, escalating the conflict with an IC to HR may easily be the breaking point that causes the team lead to be removed.
