Hazelnuts
It was only a five minute idea, and it does answer the OP question. I don't presume to have answered the prayers of all maidens everywhere, but I feel the device could have some merit.
Yes, you'd have to compute from air data, the inverse of mach computation, to get a more useful half rho v squared term. I acknowledge that any device which senses q directly would be the ideal solution.
I rather think reading the mach number local to the airfoil surfaces could be useful in some instances, for example where mach is the limiting factor, and of course the device could also be mounted remotely to get a true mach reading.
It also could monitor in three orthogonal directions to provide a full airspeed vector, providing a useful alternative or backup for aoa vanes and sideslip indicators.