> You have to distinguish the conventional (high efficiency) cycle of a jet engine at low Mach, from the reheat (low efficiency) operation usually used for high Mach.

Exactly. At high mach, almost all of the energy being put into the flow is from expanding combustion gases - not the compressor stage. If you wanted to go at supersonic speeds using only spinning fans, you will need a heck of a lot of fans. Maybe we could do it! But we haven't so far.