First: not true. The airplane will accelerate during the descent if you descent in MACH, because the same mach number provides a higher IAS at lower level, until the point you change-over to indicated and then the flight path angle will decrese and stabilize.
I have no idea what aeroplane you fly, but at higher level your airspeed margin is decresed (between min and max speed, I mean) so maintaining a constant mach provides a good safety margin. Otherwise you would have to wind up the speed (IAS) constantly during the descent to keep a good rate.
Second: the aeroplane should not overspeed until you get to the point where your cruise/descent Mach equals the max IAS of the aeroplane, and this should happen at a low level (and a good autopilot should have corrected your error already).. if it takes this long to complete a briefing there is something badly managed there...
No, I don't agree with you....sorry!!