Regarding Wizards being able to learn any spell, I initially wanted to compose an argument about how it will unbalance the game at higher levels, but you know what? It's actually not OP at all, all things considered. With a couple of possible exceptions (looking at you, Spirit Guardians), most cleric spells wouldn't be too disruptive in the hands of a wimpy dude in a robe.
The only serious downside I can see is that it's kinda stealing the Bard's shtick, since they are supposed to be unique out of all classes being able to dip their beak into other people's spell lists, which is one of the primary reasons for wanting to play a bard. To a lesser extent, it also steals some thunder from Divine Soul sorcerers, whose main appeal is being able to play an arcane caster with divine spells. It feels a bit sucky to take the one good thing these classes have going for them and give it to the class that already has the broadest and richest spell list of the game.
But no, mechanically I don't feel it would be unbalancing at all.
