Gallium-Arsenisde has a high switching speed because of the higher carrier mobility, but the higher frequency applications it is used in dissipate high power.

This article's transistors will not likely have a high switching speed, just high enough for switching power converters (100kHZ-few MHZ). The important feature of GaN according to the article is that you generate 1/10 the waste heat from current just flowing through the switch.

Power transistors don't perfectly 'turn on' like an ideal switch. They have a resistance to the switched path on the order of milliohms called Rds (resistance source to drain). And, heat dissipated from that is ~ I^2 x Rds.