How much did humanity try applying science to science itself?

For example, let's say that we have a hypothesis "if we force scientists to publish a lot, they will produce better science". Well, that's a testable hypothesis. We could take a large set of scientists, randomly split them into two groups, provide unconditional income to one group, and tell the other group they will be fired if they don't meet their quota of published research. Wait ten or twenty years, and then compare which group has more Nobel prices.

Okay, that was exaggerated, but I hope you got the idea.

In other words, I am curious about how much the working conditions, education, etc. of scientists is actually based on pseudoscience or random decisions, and how much is somehow evidence-based.