Is PIP just an American thing? I don't think they could do it in Europe, right?
It seems you have accepted that PIPs are just a tool to fire someone but still think calling it a PIP is perfectly logical and desirable to the point that you snarkily suggest that this is what it should be called.
Once someone has been employed at a company for two years, they can't be dismissed without going through a fair disciplinary process.
A PIP is a good way to demonstrate that an employee is not performing adequately, even after being given an opportunity to improve.