From Texas Instruments on output filters of Class-D amps that are set too high corner frequency.This statement is false. There are no class D amps that run without filters- such an amp is theoretically possible, relying on the inductance of the load to sort things out, but so far even with GaNFETs the switching frequencies are far too low.
"A concern with the switching waveform being dissipated in the speaker is that it may cause damage to the speaker"
This is what happened to my mates Wilson 8’s above, as Wilson does not use a Zoble Filters on this tweeter and I think all their speakers.
More likely the reason for the tweeter failure (if even real) was that the amp used with the speaker was overloaded. That's a classic source of tweeter failure!