Absolutely, employees leave bad managers, they seldom want to leave the employer itself – Or at least this was my personal experience, always on the run from dead woods.
The key for this to work is that you need to give everybody big raises so the best want to stay when the heat gets tough (like sterotypical ibanking)
That’s implying the best people choose the best pay, not the best work, 100% of the time. I quit my Big Tech job because the work sucked. There was no reasonable raise that would have kept me there, but turning DOWN the heat might have kept me there…
The worst performers know they can't get an equivalent job somewhere else, so they're going to cling on no matter how miserable you make it. They have no choice. Your best performers know they have their pick of any job they like so it anything gets worse for them they'll just go somewhere else.