What's wrong with an "overspeed"?
In an aircraft designed for subsonic flight, there is a lot of reason not to get too close to M 1.0. The primary reason is the center of pressure shift which occurs rather abruptly.
The aerodynamic center of the wing shifts from the quarter chord to the 50% chord (Actually the whole airframe generates lift based on the Angle of Attack of the individual components).
Since your lift is being generated further aft, the nose wants to tuck. The only way to get it back up will probably be THS trim since the elevator will be ineffective, but that has hazards all of its own, particularly when you decelerate below the transition point.
Then you might well break something when all that nose up trim takes hold.
If you haven't seen it before, take a look at the A380 flutter test video.
YouTube - Airbus A380 Flutter Test
In addition to Mach tuck and flutter when you exceed the demonstrated envelope, subsonic airliners buffet and occasionally lose bits off the aircraft.
It was impressive to see how much nose up stabilator (stabilator itself was nose down) was required to fly level in a supersonic F-4.