It's unfortunate that class D amps are called class D since in audio D often stands for digital and the description of how a class D amp works(square waves) sort of sounds digital. Plus class D involves encoding albeit an analog encoding not a digital one.
On top of that, they got marketed as digital amps, and some of them take a digital input and don't require a line level d/a converter. They somehow convert PCM directly into PWM to switch the amplifier on and off, so the analog signal never emerges until the PWM signal goes through the capacitor on the amp's output. They can bypass a pre-amp too by adjusting the rail voltage on the class D amplifier to control the volume. I had a Panasonic PurePath digital receiver in the early 2000s that touted all these features. It was zero negative feedback too!
Still I agree with you, the class D topology is not working in the digital domain, most clearly when being fed an analog signal that it is converting to pulse widths that are not time bound by any clock rate. With the digital input it gets a little more fuzzy for me. In that case it seems like the pulse widths are tied to some clock rate. That seems like a disadvantage, and from the measurements I've seen, class D amps set up to take an analog line level signal perform better than the ones set up to convert the PCM signal directly to PWM.