I think a few simple weapons should be finesse, like staff, spear, and handaxe.Only thing I don't like is that wizards rather use daggers than a staff and goblins don't use spears anymore.
I don't have a solution though.
Maybe adding abilities like martial arts to all classes that allow the use of finesse weapons with dexterity seems appropriate.
For one thing, those are never the best options, so it’s not gonna break anything. For another, they aren’t heavy slow weapons, so why not?
Or, all weapons are finesse, damage is strength except for monks, rangers, and rogues, who each have a feature that changes things.