I wouldn't want to see Pete leave - all things considered he's done a great job keeping the team competitive year after year despite all the personnel turnover. Very few coaches have that level of consistency - some of it is certainly Wilson, and there have been mistakes, but overall I trust Pete and John running this team.
With that said, one of his weaknesses is decision making under pressure. I don't know exactly what happened with that delay of game penalty, but assuming it was due to taking forever to get the call in, it's just another instance of indecisiveness or bad decisions in-game causing unnecessary problems. Even ignoring play-calls, which will always be debated, I have no faith in Pete to manage the clock, use timeouts wisely, make smart decisions on 4th down when behind, make smart challenges, etc.
So what's the answer for a good coach who can't think on his feet? What might help is having someone extremely analytics minded standing next to Pete to help him manage the clock, know what to do on fourth down, etc. Some of it comes down to Pete himself needing to show more discipline and stick with a decision, but I do wonder if he isn't getting the help he needs in these situations?