Let me reply for all tags, “standard” tags and MB specific tags, here. As for this discussions with standard tags I mean tags that are either formally standardized or are pseudo-standard as they are commonly used by players and tagging software.
Standard tags: Looking at the output above, there seems to be a TRACK tag. For some reason MusicBrainz Picard just can’t make up its mind and writes it all different all the times, the developers must be crazy, right? Just that there is no single TRACK tag at all. There is TRCK for ID3, trkn for MP4, WM/TrackNumber for WMA, Track for APE and TRACKNUMBER for Vorbis. To make it more complicated, for some formats this tag is supposed to also contain the number of totaltracks, e.g. in ID3 or Ape tags it is supposed to be written as “3/13”. But also the MP4 trkn tag contains the total number of tracks, just in a more specific binary format.
So to sum up: Different tagging standards are different, they use different tags and have a very different tag structure. There is no point in using “the same” tags for all the formats, what you have to do is using the standard tags for each format. And it is the responsibility of the software reading those tags to present them to the user in a meaningful and harmonized way. The output above is a nice example for this: The software used for this obviously makes some effort to present the tags for one format in a readable way. But it makes no effort to harmonize the displayed data between different tagging formats. Blame that software, but Picard is doing everything correctly.
MusicBrainz specific tags: Those are bit more complicated. Apart from a set of standardized tags all the commonly used tagging formats also provide some kind of freeform tags. Basically this allows you to store any data you want, and you can assign that data any name (with some format specific limitations) you want. Now again, there is not really a “MUSICBRAINZ ALBUM ARTIST ID” tag. There is “TXXX:MusicBrainz Album Artist Id” for MP3, “----:com.apple.iTunes:MusicBrainz Album Artist Id” for MP4, “MusicBrainz/Album Artist Id” for WMA and “MUSICBRAINZ_ALBUMARTISTID” for Vorbis and APE. Please note how the actual tags used for ID3 and MP4 are not all uppercase, as the output posted by @an3k suggests. Uppercasing them is just another arbitrary thing the software outputting the tags does (even though ID3 tags are case sensitive).
The MusicBrainz tags where chosen in a way that suits the tag formats at hand and follows common practices used for tags inside the format in question. For example Vorbis tags can contain most ASCII characters and are case-insensitive, but are commonly written in uppercase. They could contain spaces, but I have actually never seen a tag using spaces there. Now you could just use “MUSICBRAINZ_ALBUMARTISTID” and use that for all the tags (even if it would maybe look funny for a specific format), storing e.g. “TXXX:MUSICBRAINZ_ALBUMARTISTID” in ID3 (consider the TXXX just as a namespace for freeform tags here). And there are for sure some arguments for it, but as a matter of fact when the mapping of those MB tags to the tagging formats was specified it was given more care to make the tags fit in with the format than to unify them across formats.
Can this be changed? I don’t think so. The MB tags are around for a very long time, they are well specified in the Picard tag mapping and a lot of software follows these MB standards. We have gone into some effort to keep the tags stable over all the time. Changing them now would not do much good and just lead to inconsistencies and software not working as expected.
Furthermore it is usually not a really big deal. Any software reading or writing different tag formats needs to have some way to map between format specific tags and an internal representation of those tags. Doing this for MB tags if needed is not really difficult.