My understanding is that MQA is a successor to HDCD. HDCD was originally developed as attempt to add resolution above 44.1k on CDs. Higher frequency information is encoded (hopefully inaudibly on non-HDCD compliant devices) into the CD data, and removed, decoded & added back to the 44.1k data in the DAC.
It made some sense then, but we're not limited to CD Redbook anymore and often have access to even higher rez files. Now it just seems like marketing to the gullible.