The issue is: are AA and AI filters detrimental? Some say yes. Some say no. Let's worry about filters. Then let's worry some more.
MQA sidesteps this: let's find the simplest possible filter that satifies specific criteria for the music at hand. Stop worrying.
I do not see that they have sidestepped the filtering issues, at all. In the absence of a clear, unambiguous mandate for single, specific, industry-wide approach - there is controversy, as you say - MQA is offering their own approach, a proprietary one that causes alarms to go off and photon torpedo shields to go up in many heads. They have faced the filtering issue head on, extending it to the ADC as well as the DAC, unlike anyone else to date, AFAIK. Are they overreaching? Off on a wild tangent? Blowing nothing but smoke in its audible effectiveness? Perhaps. Time will tell.
The tricky part of your construct is "satisfies specific criteria for the music". There may be considerable disagreement as to what those specific criteria are. That is probably much more true today than it was when digital audio was younger. Much greater technological choice, much broader knowledge and much better measurement techniques are available today. But, there is no "perfect filter" to solve this elusive audio processing problem; they are all imperfect. Specific approaches therefore appear to diverge more than they converge, and absolute perfection will likely never be achieved. At the same time, though, my impression is sound gets slowly but incrementally better in general across the industry as techniques and understanding become more sophisticated, not schematically simpler.
I talked to a physicist once about his work on subatomic particles. His view was that a lot of what he and others did was to find ever more complex and sophisticated approaches to just extend the number of decimal places in the precision to which certain phenomena were known. That was as opposed to making new discoveries of entirely new breakthrough phenomena, though the search goes on for those to a much more limited extent. I guess he was hoping to be lucky enough to stumble across something new and big and win a Nobel Prize, but that was not happening in his own work.
Perhaps, someting similar is the best that filter designers can hope to do: further extend the accuracy and precision to the point of absolute inaudibility, though never to the impossible absolute of measured perfection. Are we there at absolute inaudibility across the recording and playback chain yet? I doubt that any digital audio filter designers think we are. Audiophiles might be satisfied, that is, until they think they hear something that "sounds better". That, or, enough marketers, reviewers and other audiophiles tell them someting "better" exists.
All the various filters out there play music. If they do not do that reasonably well, they are not implemented or they do not survive. It is much trickier to answer which approach is better, let alone "best". I do not think we are at the point yet that all DACs sound alike, myself. And, DACs with selectable filtering options seem to be increasing in number, though that option might be something of a gimmick.
So, I would like to hear for myself someday what Stuart, et al, have done here. I doubt that it is the gee whiz, colossal sonic breakthrough that Harley and others might suggest. But, I am open to the possibility it might be noticeably better than what we have. It is more radical and far reaching in its attempt than most others. I am trying to keep an open mind as I passively follow developments. It is not a life and death matter, but possibly it could offer a worthwhile improvement eventually.
Succeeding commercially in the marketplace, given audiophile and industry resistance to change, is another matter, however. And, no one will be forced to use it.