I think the problem is that you can't really know if the PIP is being done in good faith or not.

In good faith, the process makes sense, right? "You are not performing, you have been told if you do not change it will be a problem, you have not changed, this is formal notice you must change or you will be fired."

In bad faith, as others have described around this thread, it's just a performance around legal departments being risk-averse when most places in the US are at-will and you could fire them with 0 notice, so they're making a paper trail out of whole cloth with the outcome predetermined, so attempting to "work harder" to get out of it is just you giving a lot of effort when you're about to need to work really hard to find another job no matter what.