[DaveBlake]

From what you write that should help to keep my collection human-manageable without having any effect on how Kodi populates its database.

Yes human manageable, v18 can do the artist local art (if needed) separately.
 

I've bitten the bullet and tagged all albums not by a single album artists as having 'Various Artists' as their albums artist. I tried to add a "Compilation" tag but KID3 doesn't seem to want to do that, so I'm trying it this  way first. In some cases this overrides what Musicbrainz came up with, which is what section 7 of the Wiki warns against.

If you have just changed album artist tag to "Various artists", but left whatever Musicbrainz Album Artist Id tag you also had then you will hit trouble. This needs changing to be 89ad4ac3-39f7-470e-963a-56509c546377 - the mbid for matching "Various Artists".

I assume that you have done this because you want them all to appear under the Compilation node? If KID3 can't add a compilation tag then use a tool that can e.g. Mp3Tag or Picard. It is a better approach than changing album artist and associated mbid.
 

From what you write, I understand that if there are MBID tags present, Kodi will contact MB and do to my files what MB wants rather than what I want, is that correct?

No, not at all!!!
There was an idea originally that Kodi could be made to phone home and get new data from Musicbrainz if the tagging was edited (correcting mistakes) rather than users having to retag, but it was never implemented. Kodi does not do that.

What I meant was that when it finds mbid tags during scanning it uses them to gather related music files together rather than using just artist names and song and album titles. Once it finds an album (release) mbid it assumes that the file will also have artist and track mbids, and if they are missing (because a human deleted them) then it can't process the file correctly. Use them or don't, but don't leave incomplete or edit in ways that don't match the other tags.
 

Is there a reason why I shouldn't simply nuke all MBID tags (thereby essentially killing all MB support in Kodi)? I'd hate to do that because I assume that the strong support Kodi has for MB was intended to be a Good Thing, but if all it does is get in the way of my intended way of organizing my files, there's little for it.

MBIDs are useful because names are not very unique (the bigger and more diverse you collection the more likely you are to need this).
Advantages:

• They allow you to have different artists with the same name in your library e.g. "John Williams" the classical guitarist and "John Williams" the film music composer and conductor.
  
• They negate inconsistencies in artist naming e.g. having "Peter Tchaikovsky" on some albums and "Piotr Czajkowski" on others
  
• They allow you to have more than one release of an album in your library e.g. the normal and deluxe editions of an album
  
• They clearly identify the artist and album in ways that names alone can not. This can then be used to accurately pick up additional artist and album information and art (stuff not in the tags such as album review, or artist dates). e.g. which of the 90 artists called "Darius" do you want?
  
• They allow the scraping process (that fetches the additional data and art) to be more efficient, otherwise an extra call is made to try and get an mbid first to use at other remote sites, and each request from Musicbrainz must be throttled to 1 per sec.
  

 
If none of that is of interest to you then nuke away.

If you like use mbids in some albums and not in others, just don't leave partial mbid tags in some files, or in some files from an album but not others (Kodi will see these as 2 separate albums). My own collection has some albums with mbid tags and others not just from history, but now I always tag with them even making Musicbrainz entries when I rip a release they don't have an entry for.

My advice - organise the files in a way that is nice for you as a human. Tag them accurately and consistently, dare I even suggest you accept what Musicbrainz offers and see the outcome as a library before you meddle with it.