Quote Originally Posted by cadaveca View Post
but is it really the voltage increase, or the current increase that allows faster switching?

Or is the voltage a sneaky way of bypassing current limits?
As far as parasitic capacitances need charging, increasing one or the other while holding the other constant would make it happen quicker.

From the standpoint of the transistor, voltage in fact is at first directly proportional, and then a square factor for the drive current as it changes operation modes. You can check this out if you want, slides 5-8 are relevant.