The problem isn't just the scientists, it goes all the way up. Let's say we implement your system. Who decides how many 'smart professors' the Type Theory group gets to hire? What if the Type Theory and Machine Learning departments both want to hire a new 'smart professor' but the Computer Science department only has money to hire one more person?

One reasonable approach might be to look at which group has produced the 'best' research over the past few years. But how do you judge that in a way that seems fair? Once you have a criteria to judge that, then people will start to game that criteria.

Or taking a step up, The university needs to save money. How do you judge if the Chemistry department or the Computer Science department should have its funding cut.

No matter how you slice it at some point you're going to need a way for someone to judge which of two departments is producing the 'best' research and thus deserves more money, and that will incentivize people to game that metric.