Are we discussing the simple doll's head top rib extension?
Parker with Bernard I barrels, Bernard something rib and steel top rib extension...
Or the top rib bolting system?
Preacher, the answer to that question should be very evident from the title of this Thread, "Dolls head - huh - what's it good for?".
To the OP, Greener gives a pretty good explanation of the purpose and utility of the Dolls Head on pages 165 and 166 of "The Gun and Its' Development". Since we don't see BSS shotguns being shot loose under normal use, the addition of a Dolls Head probably wouldn't add much to an already sound design.