Easy to say, and I mostly agree, but it can be tough. I've seen a few of these cases of bully management and what you notice is that the team under the manager (and the teams around the manager) all already realize and communicate (sometimes just glances, sometimes quite openly) that the manager is a problem. So making a dramatic exit to make a point sometimes only makes an obvious point.

There are other factors too. Maybe you have a unique skillset and it takes some time to find similar employment, maybe you stay for family reasons, or for a (probably misguided) sense of loyalty to the team. In my last relevant personal experience, it was obviously a hostile work environment fairly early on but I had made an informal commitment to stay on for X amount of time when I joined.

Abusive managers often actually score big wins in short order and garner favor from higher management, but inevitably we see those managers burn out the systems they build and the systems around them. Employees start bouncing out at an accelerating pace and it's a compounding effect usually because an already overtaxed team is now smaller and has to pick up the slack of the departed.

It usually ends badly.

Which of course factors back into the decision not to make a public display of an exit -- karma usually finds a way to sort these things out.

I think it's probably the case that a lot of these managers are completely oblivious to their actions. I had one manager who proudly claimed (to the team) knowledge of sneaky political tactics and posted articles on fb about Machiavelli and corporate tactics for grabbing and wielding power. It's quite an awkward thing to watch and they're usually not fooling anybody.