At the expense of a small technical quibble, I don’t see Class D as entirely analog. Without the pulse-width modulator, it is a 100~500 kHz AM transmitter that transmits a silent carrier. The pulse-width modulator is what makes the whole thing possible ... the pulse widths are precisely (and I mean very precisely, down to parts per million) 50% positive and 50% negative, if the input is zero.
Deviations from exactly 50/50 alter the pulse widths (to 51%/49% or any other ratio) but the pulses themselves are rail-to-rail, and the output devices are purely switches. It is a modulation system like AM or FM, which are also analog, but it is a modulation system nonetheless. Without the PWM modulator, there is no signal that can get through the amplifier.
Class D has been around commercially since the early Seventies. The trick is extremely fast switching with no overhang, resistance to load reactance, and a (very) low-distortion modulator. An FM transmission chain that achieves less than 0.1% distortion is at the limit of the art, and PWM modulators inevitably have their own set of distortions. PWM is not inherently distortionless, any more than AM or FM. Yes, it can be transmitted, but it would be very sensitive to multipath and group-delay errors ... both would cause distortion. With both FM and PWM, small time errors translate into amplitude distortion after demodulation.
Interestingly, SACD/DSD, at the native 2.8 MHz switching rate, is a type of quantized PWM. Since the pulses of true PWM are variable width, they cannot be recorded on digital media. DSD uses dither encoding and digital feedback (noise shaping) to quantize the PWM pulse train into fixed widths and provide the closest approximation to true PWM on playback.