>>>>But that would not really work for extruding a face rather than curves, since you can't really select a face and also the whole solid that the face belongs to at once...
>>>>

Or would it???? A special face selection drilldown like the edge drilldown that is in swing when doing the extrude.. Select a solid, then on hover the faces are selectable also along with the edges (some kind of rollover like a hatch or something). Only kicks in when auto-bool extrude is in play.

Too complicated?