When loading mags the issue Tom mentions above is part of it. Another issue is with a rimless design, or a rebated rim, magazines could be relatively straight and possibly double stacked to get the capacity up. I've seen rotary mags that have 4 separate tubes that you can index which is cool but to swap those "magazines" out has to be time consuming where a box magazine would be a lot like a carbine mag change. I've had some time to exercise my Google-foo and everyone is concerned with head spacing but I thought shot guns head spaced of the rim, why couldn't they head space off the base or rebated rim?
This is more a thought excercise that may lead to something else because I'm bored
There needs to be something to physically stop the forward travel of the round at the right place to assure proper headspacing.
Since there are multiple base sizes, the chamber can't be made to have a physical stop for all different lengths.
A rebated rim on a rifle cartridge is to allow something for the extractor to grab. The round would most likely heads pace on the shoulder.
Semi-auto pistol cases like the .45 ACP head space on the front edge of the case. That is why a taper crimp is used on them rather than a roll crimp.
Some cartridges are belted ..a band around the case ahead of where the rim would be. It is used for head spacing...and would probably result in the same issues as the rimed shell when used in a magazine.
Any of these methods would require a new standard for shotgun chambers and the separation of the 'old' design ammo from the 'new'... a major undertaking and potential safety hazard.