There are several issues with MQA independent of a claim of saving bandwidth. If it had simply been presented as another lossy codec for space savings, like MP3 or Ogg, then we'd be having a very different discussion. But in that case it also would have likely been forgotten by now.
1. The way the technology has been presented and discussed, it leads to misinformation, disinformation, and misunderstandings. As illustrated by this thread.
2. From a purely technical perspective, it is a worse choice than comparable codecs for encoding, storing, and reproducing audio data (not the sound, the data). Similar to vinyl or cassettes being technically inferior to Red Book CDs. You can certainly prefer the sound of X to Y, but that's separate from any technical merits.
3. From a marketing perspective, and as a result of #1, MQA has become a feature requested by consumers that increases the cost and complexity of products. That cost is not free and will be passed on to the consumer when buying hardware, software, and music.
4. The problems MQA advertises itself as solving are problems that it is essentially creating for itself. For example, you ask if MQA helps reduce the bandwidth then isn't that a good thing (independent of any other claims or issues). But the truth is that it doesn't reduce the bandwidth required when compared against alternative codecs, for audio of equal fidelity (e.g. 17-bit/96kHz MQA displayed as 24-bit/96kHz during playback but equal to 17-bit/96kHz LPCM).
5. Unlike multichannel audio, 2-channel consumer audio was the one area unburdened by a proprietary codec. That means anyone could design and build their own product that would be both backwards- and forwards-compatible, and anyone could perfectly transcode audio data constrained only by the technical limits of a codec or medium. That also extends to audio creation. MQA changes that the same way HDMI, HDCP, MPEG-2, Dolby Digital, etc. changed things for multichannel. For video, at least, the industry has made a conscious decision to fight that in the form of the Alliance for Open Media and AV1 codec.