I own a Berkeley Alpha Reference Series 2 MQA DAC along with the Alpha USB. I think it's a little wierd to go after Berkeley when there are so many DAC maunfacturers who have incorporated MQA into their hardware but I'm going to do my best to answer your question. I've gleaned the following information from product reviews and interviews with Pflaumer and Johnson who formed Pacific Microsonics in the mid 1990's.
Michael "Pflash" Pflaumer designed the Berkeley DACs. He is best known for constructing the HDCD encode-decode process for Redbook CDs along with Keith Johnson. I have a fairly extensive collection of HDCDs and I have compared many of them to their standard counterparts. I like the feature and I go out of my way to buy the HDCD version when available. Some of the titles sound much better than their standard versions but I've never had an HDCD disc that sounded worse. Keith Johnson's recordings which are HDCD only are some of the best sounding audiophile recordings in my collection. I've owned players that had the HDCD feature since the format came out.
Pacific Microsonics (PM) who invented HDCD also made A/D converters for the recording industry. Their converters were consided the best available. One of the reasons that HDCD sounds so good is because the digital file was created with a superior converter. Digital hardware was far from mature in the 90's and Pflaumer's converters were the choice of many top musicians and recording studios. A bunch of bands and musicians went out of their way to have their master tapes redegitized and rereleased using the PM converters and the HDCD codec. Crosby, Stills, Nash, and Young, Joni Mitchell, Roxy Music, Van Halen, the list goes on and on. Whatever you think of HDCD, there were a lot of top acts that saw the benefit in it. It's been my opinion for a long time that the superior sound of HDCD is due to the better sound of PM's converters as well as the HDCD codec,
When Pfaumer designed the Bekeley Reference Series 2 he wanted to incorporate MQA because there was a demand for it. Tidal was growing fast and it had a generally positive buzz. Pfaumer tested the format and found that the code he was given by MQA was not up to his standard. His answer was to rewrite the MQA code from scratch. AFAIK he is the only designer to ever do this. In the process of writing the MQA code Pfaumer discovered some tricks that improved the coding of his regular DAC software so he incorporated that as well. The main point I want to make is that Pfaumer is probably the most qualified individual on the planet to design a DAC with MQA. He understands the benefits of an encode-decode system for improving CD playback. You are projecting your hatred of MQA onto Pflaumer (and the rest of us) and assuming that he doesn't like the process. I think your basic premise is wrong.
Regarding MQA, I'm not a supporter but I'm not a hater either. I subscribe to Qobuz because I have a fast internet connection and I would prefer to stream the full resolution files. However, even with a fast fiber connection I still get glitches when streaming a 192 file. I understand the basic reason for MQA because high res files take a lot of bandwidth.
When I got the Reference Series 2 I wanted to try the MQA feature and I was in the market for a CD transport. I bought a TEAC VRDS 701 which has the capability to play MQA CDs. The TEAC does the first unfold and the Berkeley DAC does the rest. I bought a bunch of MQA CDs to try them out. These are catalog titles for which I have the regular CD or SACD version. In some cases the MQA version is much better. The Doobie Brothers catalog is available in CD MQA format and these discs sound much better than their CD counterparts. I would even use the term "revelatory." In the case of Takin' It To The Streets" for which I have the SACD, the MQA version beats that one too. I suspect it is the remastering rather than the MQA encoding but the difference is easily heard. In other cases the MQA version is about the same as the original. Anita Baker; "Rapture" sounds very similar between the original CD and the MQA version. The MQA version certainly doesn't sound worse.
I can't help myself from closing with an editorial comment. It's kind of sad that there are people who seem to stay awake nights hating on various aspects of our hobby. If you don't like it then don't buy it or listen to it. And please, don't ascribe stupidity or nefarious motivations onto someone else who you know nothing about. In other words, get a life.