The Future of Audio Amplification

Class A biasing is the easiest to get the most linearity from a tube/transistor. The other classes are a result of minimizing heat generation, and related detrimental effects.Throw enough time and money at a problem and it can likely be solved.The biasing class does not resolve other technical issues, like sloppy power supplies, noise generation etc. It is possible to screw up any biasing class, alone it does not solve all the issues.Measurement equipment has gotten a lot better over the years, but the dB scale does not correlate to what is important in psycho-acoustics. In the early days harmonics was easily measured, and an important and fundamental measurement in RF circuits. Here decibels works fine.The human ear generates harmonics internally and may mask the harmonics from an amplifier. Much have been said on the issue of non-linearities of sound equipment, and measurement standards have sharpened over the years. As transistor amplifiers replaced tube amps way back when, measurements for tube amp were applied, and looked OK, but sounded worse. Early transistor circuits where copies of tube circuits, with inter-stage transformers and everything. Maybe a good thing as the weak frequency response of the magnetics components may have filtered out some nasties.Then the power wars started (70's?) and FTC declared that "music power" was wrong and RMS power was the way. This lead to many wrong design decisions, as music was not the way to judge music equipment. This was stupid, as these audio amps where not intended to power light bulbs, but reproduce signal with very high peak to average ratio.Since then this has been mostly corrected or ignored.The poor consumer has been told to trust the numbers more than his ears, which has lead to generations of people not being exposed to good sound.The convenience factor is more important than sound quality. Sound does not have a "look" like TV picture, where quality judgement is plain to see.The .mp3 revolution hit the whole sound world in the groin. We are still trying to recover from this, and it will be hard.
Adding insult to injury music forms have been developed that masks the poor quality of the storage formats. Synthesized music which lacks an acoustic reality is not exactly challenging to reproduce. The loudness wars have further compressed the dynamic range and will mask low resolution storage formats. Recording studios, with "impressive" looking mixer boards, will do their best to produce a "sound" (-signature) that likely is much different than a natural performance, to sell more units. Close-miking and overdubbing may be cool, but gets tiresome. Old recordings made with very simple gear may sound better than later generation equipment.Hence the trend towards retro equipment.
There is as far as I know not any objective parametric audiophile grading standard for equipment performance.
Hence too many words.Subjective evaluation is fraught with difficulties. Listening fatigue, emotions, stress, and the like makes it hard. Music is by nature emotional, which is a trap for objectivity. Equipment can sound different but still good, so what is the verdict, fidel or no fidel?
Sound buffs may want to have a nice sound coming out of their speakers, which is opposite to what fidelity is. If the source material is crap so should the sound out of the speaker be too.
There are tons of bad music compositions topped by bad performances and bad recording techniques served up in mediocre formats. These _should_ sound bad if accurately reproduced.
Good music, with good performance, recording technology and storage format, is exceedingly rare. When was the last time the hair on your arms raised up from listening a beautiful piece of music?Seemingly most people do not care, keep listening to the junk material.
Looking at high end equipment makes me think that most of the money is spent on what meets the eye.Good sound equipment should not be super expensive. If you cannot tell how it sounds unless it is big and shiny, it is not sound reproduction that is primary. 
Congratulations if you read all this, you must be very mad by now :-)

You can mess up any amplifier operating class. The specific implementation is more important.
Class A implies better quality than D or inverse F, but that "class" system is not a value scale.
Class A sets the zero signal in the middle of the operating range, as to avoid the typical non-linearities at the extremes of the device's transfer curve. This was in started in the tube age. Many later semiconductor devices had poor linearity, which was "fixed" with gobs of feedback, and transistor power amplifier output stages almost exclusively have no gain, they just operate as voltage followers/current amplifiers. So linearity biasing is not the goal here, but avoiding ugly transitions when the voltage crosses the zero point. 
There would be more work getting a D amp to perform well, but of course as this thread has shown it is possible. The digitizer must be very good, operating at a high frequency and have good filters for the output. Higher frequencies will be easier to filter out and will have more resolution. 
The bit stream output from a DAC could be used to drive an output stage, perhaps skipping some time middle pieces. Change the power supply voltage and the gain changes. 
Obviously junk in the power supply will end up in your ears.