Wilder mentioned in the ring after he was defeated that he was carrying baggage in to the ring, he definitely was not the same fighter that fought Fury in the first fight. He alluded to things on his mind that he could not shake off therefore was not fully focused.
Even if there is a third fight, I agree with you in that we will see a different Wilder but I disagree with you when you say he will not make the same mistakes. Once he is on the receiving end of a barrage of punches to the head from Fury I am sure he will not be able to control the narrative and the result will be the same - a victory for Fury.
I honestly cannot see Wilder asking for a re-match - he knows Fury will destroy him again. If Wilder manages to unleash a powerful right hand and catches Fury off-guard he might win but he cannot out box and he cannot outclass Fury therefore another defeat for Wilder is the only result. If Wilder has a few warm-up fights beforehand then tries to get a fight with either Fury then he stands a better chance but inevitably Fury will destroy Wilder again regardless.
The career of Wilder is definitely not over but he is 34 years old and even so he still has time to try to get a shot at the title again but it would be better for him to take some time out and fix those issues that he had in his personal life before he went in to the Fury fight. After that he should have two or three warm up fights before trying to set up a title shot against whoever holds the bests and anyway by then he might be the no1 mandatory fighter which would allow him to get another chance at being heavyweight world champion again.
What personal issues? Wilder was at the top of his game and held the belt, so he's not going to vacate it or have a few warm up fights with nobodies. Fighting a few bums is pointless when you can fight the best of the rest and make the big bucks doing so. I'm sure we'll see a different Wilder in the rematch and I doubt he'll make the same mistakes again.