You have your History a bit mixed...Rolled Paper with brass head cases came out at the same time as the earliest "Full metal" (Pottet) Pinfire Shotshells; But the Boxer case ( Rolled Brass foil or Paper, with a riveted Brass head) and Centre fire, soon overtook the Pinfire case.
As brass drawing techniques got better, Full metal shotshells became popular, especially for "professional Game shooters" in the Larger calibres ( 8 and 10 and 12), But paper shells were still in use also (From 4 gauge (Punt Guns) Upwards.)
Full brass was essential for tropical and wet weather shooting, as the Paper swelled in high humidity, rendering the ammo unable to be chambered.
The development of both the one piece compressed extrusion shell ( Winchester "AA" type, and the simpler to make Rieffenhauser Patent Plastic Tube shell ( able to be made on the same machinery as the Paper shells, because it simply replaced the Paper with Plastic (Tube and inner Base Wad), by the end of the 1960s, signalled the gradual disappearance of the Paper shell, except for some European and "poor country" plants, which could not afford the sahift to Plastic.
The paper shell has had a bit of a Renaissance ( Federal re-introduced them in the 1990s) for specific Target shells) but for General HUnting and Sports use, the cheaper Plastic shell is the market leader by far....Winchester even stopped making "AA" type shells for a few years, but Popular demand saw a return to the one pice extrusion shell, followed by new Case design Patents, which use less metal in the head, and also the metal cup is now Brass Plated Steel, rather than all brass ( degardes more quickly, and is cheaper. The "All Plastic" shell ( also "one Piece") has had mixed success.
Rim strenght and extraction still cause problems in Extraction in these cases. ( Auto and Pump Guns).