> from my perspective there's absolutely no reason a capable person can't get themselves out of a PIP and remain at a company.

Many (possibly most) companies use PIPs as a pretense for a firing decision that has already been made. In those companies it is a fool's errand to try and improve your performance (because performance may have nothing to do with it). You cannot win. You should feel lucky that you only seem to have encountered legitimate pips where both sides are hoping for improved performance.