Power elements will need more driving current since they need to be turned on faster (Q = I * t), since t goes down cause f goes up, I needs to increase, Q is a "constant" dependent on the power device.
The power MOSFET gate charge is shuttled once a cycle,
ditto the loss-slug as the FET transitions through the
dissipative region (zero voltage, zero current schemes
are for this). More cycles per second, more joules per
second (i.e. loss watts).