When we lump MQA with lossy codecs, we commit a methodological mistake. This is because we are not differentiating the very divergent design intents of both approaches. Design intent comes first and only after that design implementation can be contextually understood. Form follows function.
Consider, that the explicit goal of a lossy codec is to, well, loose as much data as possible, while remaining audibly transparent and they operate in the baseband. The goal of MQA is to retain all the musical Information, including near ultrasonics. The LOSSY codec is actively shedding musical data, while MQA is trying to hold on to it. These are dramatically different design intents.
With such different design intents, implementation is vastly different. Perceptual codec has a complex psychoacoustic engine that looks for and discards musical detail that is judged to be masked to the listener. MQA is much simpler - it identfies the ultrasonic music limits and encodes it into the baseband LPCM, with a bit of bit-shifting. That's it (if you remove the "deblurring" step). Outside of the ultrasonic limit and noise floor, MQA makes no decisions about music or it's perception by the listener. Perceptual codec makes decisions about music audibility thousand times every second.
One could imagine a very low compression rate audiophile lossy codec that reaches into ultrasonics and filters out the crazy noise in the DXD master to deliver exceptional sound quality. Most people would reject it out of hand.
If there is a "perceptual" goal in MQA, it's not for the listener, it's to your equipment. They are attempting to hold any code/decode differences to the original at or below our systems' SNR. Judging by various tests from
@Archimago and others, they appear to be succeding. At that point, they become practically lossless to the listener.