The overall design matters. For example a Bel Canto ref1000 (older ice module in a nice box) is not the same as a ref1000m which is same ice module + custom input section and power supply in similar nice box. Both are spec’ed at 500w/ch into 8 ohm. The ref1000m’s are the only amp I have ever owned capable of driving any speaker I throw at them to their max and never ever even comes close to breaking a sweat. The sound is smooth, non-fatiguing and totally effortless at any practical volume, another first experienced for me.
So any claim that Class D can’t do that is totally wrong. As is anyone who might claim any Class D can.
Even the TI Class D module in my $85 Fosi amp is capable of more if integrated and housed towards that end where the extra heat generated is able to dissipate.
The devil is always in the details, Class D or otherwise. Avoid drawing generalized conclusions from limited evidence much less on theory alone.