The air intake of the SR-71 engines had the job of slowing down the air flow so it wouldn't damage the engine blades.
The main job of an inlet is to reduced the speed of the incoming air to some Mach 0.4, whatever high the speed of flight is. But not because that would damage the blades, rather because the range from Mach 0 to 0.4 is the limit within which the compressor's blades (and especially their tips) work in a proper way.
If the speed of flight is higher (Mach 0.4 to 1), then the inlet simply works as a divergent inlet (diffuser): its section gets bigger and bigger, the pressure gets higher and higher and the speed gets lower and lower (the compressor thanks Bernoulli).
And if the speed of flight is even higher (i.e. supersonic), in front of the inlet one or more shockwaves form, across which the speed reduces to high subsonic and afterward a divergent portion of the inlet finishes the work reducing again the airspeed till Mach 0.4.
This is how inlets of a modern jetliner, the Concorde or the Blackbird work(ed) to supply their compressors with a relative slow and stable airflow.
Note that the airspeed seen from a blade is the sum between the aircraft's speed and its rotating speed and it might indeed becomes supersonic: this can happen for example on the blade's tips of the fan of a modern turbofan.
Supersonic speeds on blades is normally avoided due to the decrease in the aerodynamics performance: lift decreases and drag is higher as well as noise, as visible for example in the following plots from this NASA report:
And even if, just for fun, we would design a compressor with supersonic blades, after it the combustion chamber comes: combustion is an extremely slow process, so slow that burning velocity is normally measured in cm/s (inches/s). So after our supersonic compressor we would have to slow down anyway the airflow to low subsonic speeds.
Or we switch to a (sc)ramjet, but that's another kind of machine.