I don't think the hatred towards Trump particularly pushed people to be confident in Biden – Urban isn't ride or die for the Democrats, on the whole. Mostly people have seen him as the only available option given the balance of forces.
Personally I think, and thought at the time, he was a mistake to keep on and they should have been bolder in putting someone else up, not because of his age/capability but because his administration underperformed. Fact is he's up against a very marmite candidate with endless weaknesses to attack but a vigorous (rhetorical) platform for action, and the Democrats' standard model imperialism/neoliberalism was thin gruel. Same problem in fact that every centrist government has been having. A younger more go-getting face should have been an obvious strategy to offset that problem.