It was banned in two steps. In 1920, players could assigned up to two pitchers to throw the spitball. After that season, 14 players were grandfathered in and allow to continue throwing a spitball. Burleigh Grimes threw the last legal spitball in 1934.
Carl May threw a pitch that killed Ray Chapmen in 1920, which the spitball rules still allowed teams to have spitballers. May was generally a wild pitcher, in fact he had hit Chapman's teammate, and manager, Tris Speaker in the head in 1918. May's claim was Chapman was crowding the plate, He throw a high inside fastball, that his May's teammates claim was a strike, to brush him off the plate. It was an unwritten rule about brush back pitches that lead to Chapman's death. Chapman's death had nothing to do with getting the spitball getting banned.
Rivera was the best pitcher I have seen in throwing a cutter. His long fingers let me get unique grip on it.
The problem that MLB didn't see was that my providing information about spin rates, pitchers would be able to start experimenting, see results, and adjust.