We did keep him too long once he was here, we he should have gone the summer before he did - a better manager might have helped use the money we were throwing around more wisely, and kept us up. However I would argue that not appointing him at all would have been better for the club in the long term.
Yes, we had more time in the Premier League, but thanks to the mismanagement in that final year, we didn't even really have a sound financial footing to show for it. If we'd gone down under Irvine, with Peace still in charge, it would have forced a change. Peace would either have had to sell at a lower price to (probably) a more interested party, or he would have had to focus on finding a new long-term vision for the club (aka a new Dan Ashworth).
Instead, the short-term approach of Pulis kept us up, effectively to the long-term detriment of the club as a whole.