I remember under Monk we were woeful against Leeds and got stuffed (3-0 I think). He dropped Clayton for that game and we had no bite about us at all. I agree with you that Clayton has to play tomorrow night.
Under Karanka, Adam Clayton was arguably the best DM in the league, and okay he has never recaptured that form, but tomorrow night against Leeds, if you want one player to get stuck into their midfield and go in where it hurts and never pull out of a challenge then Clayton's that man. We lose far too many 2nd balls, so no question, in my opinion Clayton would definitely be in the side tomorrow night.
Thing is mate, he's a young manager. We can argue whether that means he deserves any more credit than the manager with experience or not for sure but I sincerely doubt he's looking at his situation thinking "I can't be a manager". He doesn't seem the type. As I said, he's stubborn. He didn't make it as a quality defender saying "Sod it, I'm done" at every set-back he had... and he had plenty! Players and managers generally have more desire and determination than that. After all, even if he is sacked it doesn't mean he won't make it as a manager.
There's only one way that Woodgate 100% doesn't make it as a manager and that's if he gives up.
I understand where you're coming from, it does take a certain level of character to admit you can't do something. Not every person who walks away from something is doing it because they're cowardly, sometimes it is an intelligent thing to do. I don't think it is in this scenario for his own career.