Common Gate For Power Mosfet
If the gate is set at maybe 10V (fixed) and the source is hit with a 20Vp-p square wave (0V to 20V) then I can see good reasons to trial it - the MOSFET would turn off very quickly because the gate would be taken negative with respect to the source and to turn the device on the source would be at 0V.

However, the source signal is having to conduct the same current as the load so this is its chief disadvantage I reckon. If the drain current is 10A the signal at the source has to cope with 10A when it is low falling to virtually nothing when the source is high.

I'm not saying that there is a big power loss in the drive signal, just that the drive signal has to cope with a rapidly changing load.

Of course on the use of a common gate, any CMOS op-amp using MOSFETs as the differential pair uses a common gate by virtue that the sources are connected.

It's an interesting idea.