But they're not on the manager's side either. What rational HR department would want to keep a manager who makes their subordinates feel unsafe, work ineffectively, etc?
Any of them, because:
(1) The manager is more likely to know their legal rights,
(2) The manager is more likely to be able to afford the cost of litigation in a dispute,
(3) The manager is more likely to have a contract beyond at-will employment,
(4) Determining whether the manager is a problem or the employee is malingering has a cost, plus risks creating evidence of corporate liability
Etc.
Except in the most clear and egregious cases, HR is naturally aligned with management against the human resources that management manages; that's kind of the point of HR, whose function is to assist management in efficiently (i.e., at minimum cost per unit value produced) managing those the human resources.
HR is not a neutral referee; the closest there is to that is government labor relations authorities.
Sure, it might work most of the time. But the one time it doesn't work, could cause billions of dollars in damages.
Just look at what happened to Uber after they retaliated against the wrong "low level" employee.