I do not want more classes, I think there are already too many. I'd at least get rid of one of the arcane trio of wizard, sorcerer and warlock. I think Warlock chassis is cool, but the class is too mechanically and thematically limited. Sorcerer on the other hand is mechanically rather pointless. I'd remove sorcerer, and broaden warlock so that it can also represent sorcerer concepts. I would also try to lessen the impression that warlock is the generic 'creepy arcane caster.' I would remove book pact stuff from warlock and give wizard more options to be a creepy occultist messing with forbidden spells.
As with monks bards and monks, I'd make bard less magical and monk more magical. Let the monk be amazing wuxia martial artist with mystic powers, so a half-caster probably. And whilst Bard works pretty well, I think we have too many full casters, and bard now plays too much like wizard or sorcerer. Too casty, not flighty enough. I feel the bard should be a half-caster gish.
Overall, I'd increase the amount of stuff subclasses bring to the table, and ad subclasses to represent missing concepts. However, subclasses should be pretty broad and flexible too, rather than weirdly specific as they often are. Totem barbarian is my go to example of a subclass done well. It is thematically very strong, but mechanically flexible. At every step you get a choice of several features, so you can build many different sorts of totem barbarians.