Acceleration of a supersonic aircraft after breaking the sound barrier
Your Taylor expansion only uses the first two terms, so it is only a crude approximation. But still, your observation is correct, however, whether it applies depends on the aerodynamic quality of the particular aircraft.

Practical supersonic aircraft have been designed to minimize the Mach drag peak. The ways to do this should be familiar:


Stretch the aircraft lengthwise so it becomes long and thin.
Smooth out the cross sectional area distribution over length ("area ruling")
Use swept wings with thin airfoils


If this is properly done, the drag peak will be small enough to have overall drag increase with Mach number above Mach 1. In case of the F-16 the drag coefficient rises from 0.02 (subsonic) to 0.045 (Mach 1.1) and stays roughly constant with increasing Mach number, so the absolute drag still grows with speed squared. No significant decrease in the drag coefficient occurs because of the complex flow
around the entire aircraft. Only when you have a poor design will drag actually become lower at low supersonic Mach numbers.

Another factor is thrust: Since ram pressure at the intake increases, so does thrust of the same engine as speed increases. This is the main reason why Concorde could already super-cruise 20 years prior to Lockheed marketing inventing this term.