Then the company hires a stooge CEO that happens to have "coach", and if they don't listen to their "coach" the board fires them. Or the CEO gets handed a board seat or side consulting gig from a key investor. Etc.

You can certainly try to address this, and I'm not saying it isn't worth trying. But I do think you'd be playing whack-a-mole with creative management consultancies and accountants trying to find workarounds for a very long time, and you'd need to be prepared for that.

It also doesn't really address the problem so much - while CEO pay is often entirely out of proportion, the money flow to investors is often a far bigger issue, and would also be a workaround: Ensure the CEO has enough shares, and gets to sell enough shares, and they have a vested interest in doing the work even with lower pay. E.g. there are plenty of CEO's on low pay because their ownership is sufficient.