Underpowering is not a myth when you are pushing the Bass Amp to 9 and 10 positions on the volume knob reaching for 11.
It was commonly known in the past that the power sections of amps started to create direct current type power at the upper ends of operation and that attribute of the power would arc off the coil and thus "blow" the coil by an actual burn.
Long ago we had a system we worked where the band leader insisted on running 4 EV 12Ls with one side of a Peavey CS8400 Amp. We were regularly replacing voice coils on that rig,
Meanwhile he was running 4 Gauss 18" speakers with one side of the CS800. On that side of the amp we were regularly replacing power transistors that were being melted as the Gauss speakers could be plugged into 110v from the wall without melting the voice coils. Something had to die and the transistors were the weakest link, the end.
Cone extrusion is another thing completely where wattage and frequency collide to flab the cone forward. Never seen a grill need to hold an extrusion back.
The amps we have been working with have a limiter filter for the extrusion events, so we do not see that anymore. Also, we have not had to replace blown speakers since working with that system so long ago,
As for over power...
One of the team had a cabinet he had built for himself that he later sold to Adam Nitti. That thing was regularly run with a Crown MicroTech 1000 Power Amp where one side ran 2s JBL 8110 5" Speakers at 4 ohms, and the other side ran a JBL 2255 15" and he never blew a speaker. In fact Adam played that cab until he signed with SWR, which was before Aguilar.
You might disagree with the nomenclature, but the principles have been applied for year by our people and also friends formerly with ShowCo when that operation existed, and has kept tragedies a bay for years.