One of the benefits of completing a PIP might also be signing off an internal transfer to a team with better fit. There could be times where it's worth going through it to get something better - as long as you're quite far detached from the previous team.
There are plenty of idiots involved in hiring, that's certainly true. But I was recently (for the first time in my life) had to hire a lot of new people for my team, and I noticed I hire people on probably very different traits than some recruiters and managers do. I don't like candidates who just give socially acceptable answers, I do like candidates who give creative answers, who are vocal, opinionated, weird, outside the box and against the current. And I'm well aware people sometimes get fired for really stupid reasons. I doubt I'm the only one.
With that criteria, I would never be able to get my team complete. Most of the time I get existing employees transferred to me, I have to accept what I get or do the work myself (which is not possible). With new hires it's not easier, I interviewed candidates for 6 months without finding anyone (we don't pay so well, even if we are in top 50 in Fortune 500) and some director simply transferred me someone to fill in the role. I am just a senior manager, I said no but I was overranked and overruled.