It seems the logic behind an "Emailed Photos" album is that is where Photos attached to Messages are stored (not in Messages) - which would explain how they are only counted once against Storage limits.
Emailed Photos can be viewed in that album, or by clicking on the thumbnail displayed with the message in the Messages archive.
Why it would be desirable to be able to move photos from the "Emailed Photos" album (to 'custom' albums) is they may be of a particular Event and/or posted by multiple senders. To be able to have all photos of an Event in an Album titled with the event's name (and perhaps date) makes finding them easier than wading through all the photos ever sent attached to Messages.
Management of Photos would be much, much easier if they could be moved and organized (as Files can be). However, moving Photos would change their links (as it does with Files) and I'm guessing that makes it awkward for Groups.io to keep them linked to the message they originally were attached to.
Michael
Michael Pavan