I know this forum is suspicious of managers on general principle, and that’s sometimes appropriate, especially the more layers there are between decisions your manager is executing vs where they were made. That said, it is my experience that some managers truly want people to improve when they’re operating below expectations at a given level, and furthermore that some people need that feedback written down, formally, for it to really land and produce change.
I am happy to accept that the majority of cases where you’ve gotten a formal PIP that HR is involved with will end with the employee’s termination. I don’t have industry data on this but it would match both my actual experience and the experience of my peers as has been relayed to me over the years. But someone in that situation should be open to the possibility that they can truly succeed if the dominoes fall correctly. There are many signals along the way that will also inform you what your manager in turn believes and even HR sometimes gives themselves away despite the legal risks they are trained to avoid.
Finally, there’s a spectrum of how people use the term PIP. At the far end is what you’ve described, a written document that exists to provide evidence in the event of litigation and is largely HR driven. However a manager can absolutely use the same structure and terminology and never involve HR and hopefully we both agree those are more likely to result in win-win outcomes. In fact the trend in this space is towards a continuous performance management environment where expectations are formally defined and updated and checked in on at least quarterly if not more frequently.