It's a relevant question because the "stability" argument always finds its way into the conversation. There's no point in worrying about stability if the current staff is going to hurt the program by staying.
I hear what you are saying, but I don't totally agree. Firing Duzz could very well lead to a new coach that is more successful with Pitt ending up in a better place. However, it could also lead to another round of WTF decisions, and if possible make Pitt even more of a laughing stock.
Look at Wanny. In hindsight, he should have been retained. The end result was worse than keeping him. Of course, dipship Peterson was a big reason for the multiple clusters, and he is not longer destroying the program (although he presence is still felt).