That fact your reply to a comment about having a structured way to fire someone could be called a "performance improvement plan or PIP for short" is hilarious to me.

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.

I don't know about your situation, but at every company I've ever worked for, firing a report for performance reasons requires the employee to first be placed on a PIP. Call it whatever you want, but in most cases (from both the employee and manager perspective), a PIP is not designed with the intent that the employee should remain at the company.