What a train wreck... Following is my opinion/memory...
There were some really great class-D amplifiers decades ago, as others have noted, such as the Sony unit
@restorer-john showed us. And some pretty lousy ones of the same vintage (Infinity's I think? The one that self-destructed with capacitive loads...) In the late 1980's through 1990's IIRC the number of class-D products grew, but were rarely accepted by "audiophiles" and were found more in car and industrial/PA/sound reinforcement applications. Certainly Crown and others developed some great designs for pro audio use. I am not sure when self-oscillating designs were
first developed or by whom but Hypex and ICEPower became big players. I think (not sure) they managed to commercialize the technology with a high degree of success, due largely to closing the feedback around the output filter and thus providing lower output impedance and distortion over the full audio (plus) bandwidth. That was early 2000's best I recall, probably when class D started to make inroads into the mainstream audiophile market.
We are still running a Crown K2 at church. I do not think it is class D but am not 100% sure. I think they called it a "current amplifier" or something like that. My impression is it is a low-bias G or H design but I really don't know, not sure I ever did. Life was focused on other things then though I did help set up the system.
As for amplifier classes, the Wiki article is decent, and below is the post I dredge up whenever this comes up. Note some have argued my use of terms such as "bias current" in describing the classes; when I was designing them that is how I thought about them and, well, old dogs... The classes are named in the order they were developed, A being first and H the last, at least for now. The D is not for "digital". Crown(?) defined a class-I topology that appears to be sort of an interleaved class-D scheme but I do not think it has been officially recognized by any standards body. Interestingly enough I used a similar scheme for an RF amp long before I knew about the "class-I" audio version; I did it as a science experiment trying to get high efficiency RF amplification without needing device bandwidth beyond what was available at the time (early 1990's).
Amplifier Classes
Here is a summary from memory so don't hold me to any mistakes:
Class A = bias current flows through the output devices all of the time. Most wasted energy and heat, max theoretical efficiency ~50% for a push-pull design (only ~27% for a single-ended design IIRC). Commonly used for low-level circuits like preamps and power amp input and driver stages, rarely for output stages since it is so inefficient. More common in tube amps these days, I think.
Class B = bias current flows half the time, so in a push-pull design one device is on and the other is off. Typically one device amplifies the (+) half of the signal and the other the (-) half as it swings around ground (0 V, or a common bias voltage). Can achieve ~67% SE, ~78% push-pull efficiency in theory. In practice there is crossover distortion around the crossing point as one device is switched off and the other turned on since it does not happen instantaneously. Used for some power amplifiers in the past (do not know about today), with feedback used to reduce crossover (and other) distortion.
Class AB = biased in class A for small signals then moves to class B. This lets small signals around the crossing point stay in class A for lower distortion, then as the signal increases and moves out of the small signal region transitions to class B to save power.
Class C = bias current flows less than half the waveform cycle. The "missing" energy is usually generated by a resonant circuit (e.g. inductor/capacitor (LC) tank). Common in RF circuits where high power is needed and distortion less an issue, and oscillators which are narrow-band (audio is very wideband, spanning multiple decades) and incorporate a resonant circuit by design.
Class D = bias current flows only as output devices switch states, in a form of pulse modulation (pulse width, frequency, or both). Can achieve >90% efficiency. The high switching frequency is provided by a clock source or (for most audio amps) is self-generated by the circuit. The output pulse train is filtered so only the fundamental signal remains. See
https://www.audiosciencereview.com/forum/index.php?threads/class-d-amplifiers-101.7355/
Class E, F = utilize switching as well but constrain the switching to certain points in the signal cycle (e.g. at voltage or current zero crossings) for higher efficiency since less power is dissipated in the switching transistors. These are used exclusively in RF circuits AFAIK. Class E is used in tuned amplifiers (narrowband, again) and class F is used for generating harmonics of the fundamental so you can say build a high-frequency oscillator output from a lower-frequency circuit.
Class G, H = wrap a varying power supply around the core (typically AB) amplifier to improve efficiency. By changing the power supply voltages it uses (wastes) less energy for small signals by applying low supply voltage, then increases the voltage as required as the signal gets larger. Class G uses discrete rails so the power supply switches between two or more (high/low) voltages. Class H uses a tracking supply that varies continuously with the signal level.
There are some more esoteric classes I am not familiar with. I have only designed and worked with the classes above.
HTH - Don