In some ways, this is great. It shows that fund executives' interests are aligned with the long-term returns of the fund. It shows they are there for the carry returns and not just the annual admin fees. It gives execs skin in the game.
Serious question - are there really many bad ways to bump up the stock price?
There is financial engineering (like stock buy-backs), you can just disallow that and remove the problem.
There is unnecessary M&A, but if the employees are running amok with unnecessary M&A, you have much bigger problems.
There are illegal things -- but we have the law to take care of that.
There are extractive measures (e.g., squeeze blood from workers, suppliers), but if that is allowed, then the "value" you see from that is likely also "value" you'd reflect on the annual bonus.