Here's ancedata, from a manager's viewpoint. tldr: Over my career I've put two or three people on PIPs, at a couple of different orginizations, and it never worked out.

In all cases it was driven by me, based on my assessment of suitability and the effect on the team. I don't recall them being driven by HR, stack-ranking, pending RIFs, or any other larger organizational concerns. It was always the last-ditch effort after one-on-ones, reviews, coaching, looking for other more-suitable positions in the company, and other less-formal efforts had failed. In each of the cases I didn't have high hopes.

From my standpoint, a PIP was primarily a procedure where I documented requirements as concretely, clearly, and objectively as possible. They were tangible goals for the employee, rather than a vague "you need to do better". I thought of them as if (when) it didn't work out, then the person would know it wasn't something personal, or reflected their worth as a person, but just that they didn't fit the requirements for that job. Was that actually any consolation, or was it just rubbing the person's face in "you failed, you can't do the job"? Sigh... I don't know.

I also don't know if, years later, I'd make the same decisions in all cases. With experience I've come to appreciate more factors other than raw technical competence.

edit: Regarding time frame--once they were put on a PIP it was a several month process, but shorter than six months.