I would like to see an option to merge photos for multiple exposure in the Photo Merge section. It could have the typical options for merging, such as Additive, Average, Bright, and Dark.
You may want to expand upon that, and give more/better examples/references. And can you include any post processing software that has this capability in it as examples.
You are correct. Not HDR, not Panorama, and not HDR Panorama; but an additional Photo Merge option called Multiple Exposure.
The Multiple Exposure option would merge two or more photos (suggested maximum limit: three to five photos) using the blending modes as described in the link you provided. Those modes are generally referred to as Additive, Average, Bright, and Dark.
I don't know what post processing software may already have that capability. I use Lightroom Classic exclusively, with an occasional edit in Photoshop. I don't like going from Lightroom to Photoshop because I don't like having to save it back into Lr as a TIF file. I wish Ps saved the image back to Lr as a DNG (but that's the subject of another suggestion).
To the best of my knowledge, a multiple exposure merge can be done in Photoshop, but it is a manual process. Canon EOS cameras (and likely Nikon) provide the in-camera capability to merge multiple exposures, but you have to know which photos you want to merge beforehand and the process is a little cumbersome.
Having multiple exposure merge capability in Lr would allow the user to choose whichever photos he or she wanted for the merge (within the same folder), then select Photo Merge > Multiple Exposure. Within the Multiple Exposure screen, there would be four merge options: Additive, Average, Bright (or Light), and Dark. In practice, this would be similar to how you have options for selecting different stitching perspectives in panorama merge.
The big advantage of using Photoshop for this is that Photoshop can keep the images separate as layers (if you save the image as TIFF or PSD), giving you the option to change something at any time. Lightroom does not support layers however, and the DNG file format does not support layers either.
Another benefit of merging multiple exposures in PS not in LrC, is the availability of such algorithms as "Median" - which would probably never fall within ACR / LrC's scope, having more to do with image content than with image adjustment.
Median allows e.g. eliminating all traces of occasional people walking through, from an extended-time series of photos of the same fixed scene.
All of those Ps advantages also apply to HDR and Panorama, yet Lr offers those features, too. Why draw the line at Multiple Exposure merge?
Another advantage over in-camera Multiple Exposures is that you'd be able to try it using different blending modes on the same images. In-camera, once you've selected a mode and taken the shots, it's done. You can't undo it to try a different mode. If you used a saved base image (Canon allows this) as the first image, you can always re-snap the subsequent images using a different blend mode (we're talking in camera), but conditions change, objects move, light is fleeting.
"All of those Ps advantages also apply to HDR and Panorama, yet Lr offers those features, too. Why draw the line at Multiple Exposure merge?"
True, but in HDR and panorama the desired outcome is usually clear, so the user can leave it to Lightroom. In case of multiple exposures it is much less clear and subject to personal preference. That makes multiple exposure something I would always do in Photoshop, so personally I would not be interested in such an option in Lightroom. I would rather see Adobe add focus stacking, for example. BTW, I do occasionally use Photoshop for HDR and/or panorama too, however.
"Another advantage over in-camera Multiple Exposures is that you'd be able to try it using different blending modes on the same images. In-camera, once you've selected a mode and taken the shots, it's done. You can't undo it to try a different mode. If you used a saved base image (Canon allows this) as the first image, you can always re-snap the subsequent images using a different blend mode (we're talking in camera), but conditions change, objects move, light is fleeting."
I read this as a confirmation that using Photoshop with all it's options is probably a better idea than having a much more limited option in Lightroom...