What prevents a Machmeter from being the standard airspeed indicator?
Machmeter-based tachometer would not indicate something between IAS and CAS, it would indicate TAS but for the same¹ instrument and position errors the normal airspeed indicator has.

However, airspeed indicator does not indicate true airspeed and this is intentional.

The EAS, that the airspeed indicator is aiming to show, is a measure of dynamic pressure. Since lift, which also includes effectiveness of control surfaces, is proportional to dynamic pressure and drag is also a function of dynamic pressure, most handling characteristics depend on the dynamic pressure. Therefore the value indicated by the airspeed indicator is exactly what the pilot wants to know.

The only effects that depend on other speeds are aeroelastic flutter, which depends on true airspeed, and compressibility effects, that depend on Mach number. Both limit the maximum safe speed. That is why fast aircraft also need Machmeter. But they still need the indicated² airspeed.



¹ Both instruments use the same two raw values obtained from the pitot-static system: total and static pressure. The airspeed indicator shows square root of the difference (because dynamic pressure is proportional to square of speed), the Machmeter shows the ratio to some fractional exponent. So all the errors affect both the same way, and in electronic instruments, they are compensated² to the same extent.

² Electronic systems in modern airliners say to show CAS, correcting all errors they can reasonably estimate.