Perhaps the real problem in 5e is that there are too many core classes?
I don't agree. Actually, I'd like to see at least two more added: the Artificer and a revised Warlord (or similar - I like the concept, not necessarily the name).
But, for the sake of discussion...
My top two candidates are the Paladin and the Cleric. For me, the Paladin was always tied tightly to that problematic alignment restriction. Remove that restriction, and downgrade alignment to its current vestigial state (such that it really should be removed entirely - Traits, Bonds, and Ideals now do the same job better), and the class becomes redundant. It should be rolled into either the Cleric or the Fighter, or a combination of the two.
But I also think the Cleric was a misstep - it should have been based much more strongly on Peter Cushing's Van Helsing, and so very definitely
not tied to religions (fantasy or otherwise). Of course, that's probably one for the time machine.
I think I'm going to go with the Paladin.