HERE is a link about intakes and shock waves you might find interesting.
It's one thing to drive a transonic aircraft using a high bypass fan engine to low supersonic mach numbers in a steady state dive. It's quite something else to then ask that engine to behave nicely at high angles of attack both in pitch and yaw or to expect to operate at even higher mach numbers.
To cite one example of supersonic fan engines, the F-14 intake was a marvel of efficiency back in the day, but it was VERY complicated. The TF-30 didn't take kindly to uneven pressures across the face of the compressor/fan. So, Grumman's answer was the fancy intake system discussed
HERE. Part of the reason for a complicated intake is that unlike some high bypass afterburning engines, the fan air was not bypassed around the outside of the afterburner but was fed into the air exiting the turbine. In other words, the fan air fed the burner too and that tended to make the already fussy engine more unstable; hence the need for a sophisticated intake to insure good airflow under all conditions including short periods of flying backwards. I flew that aircraft and I still remember the "tail slide" which was part of my first familiarization flight; no big deal as it turns out. I also remember the engine failure I had on the first flight.
Again no big deal but something of a disappointment.
If there was any way to make this engine behave properly with a simple airliner-style intake, believe me they would have done so. I suspect the intake system and it's associated software cost more then the engine.