Maybe that other request to add taxonomies to media can help with this, actually.
One could put the media in whatever folders the system wants, but we still could get the media by specific criteria, and at least narrow the pool down to a few only (like: user-mugshot term), then run a title match against the pool and find the image we need.
That could work, without a lot of changes to the folder structure (could already work now, since you can easily add terms to media, you just need to declare it programmatically at this point)
Not useful if the media is uploaded in the front end thou, but better than nothing…