I also enjoyed and beaten Crypt of the Necrodancer. In fact I've written up something about it when we were talking about Roguelikes... somewhere, and my problems boiled down to the rhythm forcing down complexity of the strategy.
It would depend on how the rhythm part is implemented, but I feel having most things tied to a beat would constrain the viability of actions, and many inputs used in traditional character action games are arrhythmic and reactionary (which is difficult to do when you're buttoning to a beat). If you put emphasis on the rhythm part (like actions just fail if you don't hit a button to the beat) then the action will be railroaded and it would soon turn rote. If you put emphasis on the character action part, then the rhythm part might not even be there because all it does is encourage suboptimal/slow play and discourage freeform inputs. Then at that point you might as well either make a pure character action or a pure rhythm game.
I can bring up some hypothetical examples if you like, but I might've gabbed on about this too much.