Thanks for the feedback!
The wizard class is actually an unlock, you unlock it by completing your first run. The Warrior is currently planned to be unlocked if you complete Mastery 1.
I think the class system is probably here to stay, the majority of feedback I'm getting is positive. I am thinking of adding a 'Mimic' style class that uses random talents from all classes that can be unlocked after completing the game on all classes though. Maybe that's what you're looking for!