I think a lot of the larger and/or more powerful calibers would produce too much pressure on the action. a .73 bore shotgun at has a .42in^2 surface area, at 11500PSI that produces 4800 pounds of force on the action. That's the SAAMI limit.
a .44 magnum has 0,144in^2 of surface area, at 36000PSI that produces 5200 pounds of force. Already over spec for the shotgun. These are available - a bit odd since they could in theory produce excess pressures.
.45-70 has 0,165in^2 of surface area, at trapdoor levels of 28000PSI you'd get 4600 pounds which is OK, at lever action levels we'd have 6590lbs. Well over the limit.
30-30 has a case diameter of about .40, at 42000PSI we have over 5200lbs of force on the breech.
.308 can produce over 9000 pounds of force on the breech face.
I feel that for safety's sake thing should be limited to the lower pressure pistol rounds. Even 7.62x39 and .223 would exceed SAAMI rated breech forces in a shotgun barrel