One thing that I've been doing is using the GAME*.GOG files to install the games cleanly to a dosbox-x image (since the GOG/INS files are just rebranded bin/cue sets). This has worked for most of the games in my collection, but when I do this for World of Xeen the installer doesn't recognize the disks as World of Xeen disks.

While this doesn't affect how World of Xeen works "out of the box" it does change how I have to play the games (since my main machine is a linux box, and doing this lets me bypass the tightly-coupled but badly-optimized pre-packaged dosbox instances as well as play retro dos games that don't have linux-specific installers yet).

Is there a "known" reason as to why the GAME*.GOG files for World of Xeen are deficient in this way?

I'm not sure if I understood you correctly: have you mounted the two disks into DOSBox, then launched the DOS installer and got the error afterwards?
Honestly I have never tried this procedure and I'm not sure why it should fail: as far as I know, the two files provided by GOG should be exact copies of the game's two CDs.

By the way you may want to know that World of Xeen is playable in ScummVM too.

That is correct - I download the files via GOG Galaxy, mount the GAME*.GOG files in my local dosbox install, and attempt to run the installer, which claims it cannot find any World of Xeen CDs in the drive (despite being run from the mounted CD images)

You might try taking those files from the WORLD subdirectory of the main game folder.

What I noticed, running the game under Debian's version of DOSBox, default configuration (not the one GOG provides), is the follows:
* Running XEEN.EXE from the main directory will start the floppy disk version of the game.
* Running XEEN.EXE from the WORLD subdirectory will display a message about the CD-ROM not being found. (Mounting the CD-ROM might fix this.)
* If XEEN.EXE from the main directory (floppy version of the game) can't find XEEN.CC, then you will start Darkside of Xeen (floppy version, but without Clouds installed).

I was able to find physical copies of a World of Xeen 2-CD set for sale online (unfortunately they're the 1998 global star reprint and not the original NWC pressings, so as far as archival goes it's a bust but for my purposes they'll work), they'll arrive in a couple weeks. Hopefully I'm making a valid assumption and that the CD versions bypass the copy protection that fires when you try to leave Vertigo for the first time (and apparently when you try to enter Newcastle for the first time? I never managed to get that far), otherwise I'll just fall back to using the GOG-provided floppy version.

I wonder what pressings GOG sourced the CD version from?

The problem with the CD version is that you need the CD in the drive in order to play, something that the floppy version does not allow.

The GOG version has one difference from the ohysical CD versions. In the CD versions, at certain points the game tells you to insert disk 1 or 2; in the GOG CD version I believe it tells you to press Alt+F4 instead.

In the GOG version, there's a file in the game directory, a pdf file whose name starts with "keys", which contains all the copy protection answers for these games. (It also has the answers for MM3's copy protection, but the GOG version is cracked and skips past the screen, which is nice because the MM3 copy protection comes up at every single boot, rather than maybe 3 times during the entire game.)

ctrl-F4 is the hotkey for swapping disc images in dosbox. They just edited the text to make it more user friendly.

Xeen on CD does bypass the copy checks. If you don't want the physical disc in the drive you can do what gog did and make an image of the discs you bought.

What is your goal here? I found that the GOG installer lays down a working version of Xeen's data files and, with a few fixups to the provided DOSBox files (mostly where GOG used the wrong capitalization for filenames), it is quite playable under a Linux-hosted DOSBox.

For the floppy version, you don't even need to do that. Just use the main dosbox file (not the one with "single" in its name, mount the drive, and start xeen.exe manually and it will work.

Ultimately, the goal is to replicate the install process. The GOG-provided CD images for World of Xeen doesn't let me install to a "clean" environment, and so far World of Xeen is the only game that GOG provides that I own where this is a problem. I can do this with all four of Wake of the Ravager, Warcraft 1, Dungeon Keeper, and Heroes of Might and Magic 2, but for whatever reason I can't do this for World of Xeen.