The total power needed to drive a MOSFET gate is:
View attachment 136726
Driving a MOSFET a typical gate drive voltage will be 10 to 12V, while driving a GaN device the gate driver voltage will be 5 to 6V.
Another thing to factor in is that the total gate charge for GaN transistors will be lower than that of an equivalent MOSFET.
In summary, even though the switching frequency goes up by a factor of two the power needed to drive the gate will still be lower than for a MOSFET at a lower frequency.
Here is a very good app note on the subject:
https://www.ti.com/lit/an/slyt664/slyt664.pdf
For my design the total gate drive power needed is about 65mW per GaN FET x 4 = 260mW. I have verified this by measurement.