Designing a linear regulated dual-rail power supply
Simulating it shows the correct output voltages, but what are the
  drawbacks to this design


No it won't work very well. Reason: the load could be asymmetrical and try and lift the mid-rail point towards V+. This is highly likely in an audio amp.

The way the lower regulator is configured means that it cannot prevent this from happening because no matter what it does, its pass-transistor cannot act like a shunt voltage regulator to pull mid-rail back to the mid-point.