If the measurements show low THD with a 20 kHz signal at full amplitude then the scenario you describe (slew induced distortion) does not exist. There is no music with faster transients.If one listen only to static sine waves, then that one surely will be happy with a class D amplifier, especially if fed by a delta-sigma DAC.
Because measurements show that, and nothing more. Static signal response.
For me, because I listen to variable musical programs, with lots of transients, I feel that both class D amps and delta-sigma DACs lack in their dynamic response to transients. The closed loop of their respective converters will add distortion on that transitional phase, until they settle to the new value of the sin wave. And this keeps happening all the time, because music is variable all the time.
The means to prevent slew induced distortion is a low pass filter at the input of the gain stage with the closed loop. That is known since at least 50 years.