Why do you say 308, 30-06,243 are a mistake, is that they are often higher pressure than what a double rifle type action can take?
Pressure is always something to keep a eye on with break open guns as they are not as strong as bolt rifles. Some doubles will hold it and some will come off face quickly.
But regardless of pressure you really want a rimmed/flanged case for ejection/extraction.
Compare the systems on two guns made by the same mfg, one rimless and one rimmed. The rimless version with the spring loaded tab looks fragile and only grabs a tiny piece of the case. Sooner or latter it will fail to function correctly.
