why can't the engine accept supersonic air?
In subsonic flow, the pressure waves moving upstream from an approaching body have time to cause the air to get out of the road, as it were, without too much disruption ..
However, in supersonic flow, the approaching body comes on the scene without an introduction and the flow, in deflecting abruptly, generates shocks. These are undesirable due to energy losses but can't be avoided. Hence the effort which goes into designing intakes to function as efficiently as practicable.
Now, if the incoming flow to the compressor were to be supersonic, the interactions would be complex to the point of chaotic.
The Concorde threads have plenty of commentary on intake design and might be worth a read.