The Cardinals, as an organization, are a team that usually has a Hall of Famer on their roster. This has been true for a long, long time. We may not know it at the time, but eventually most Cardinals roster have at least one Hall of Famer. From (probably) Yadier Molina to Albert Pujols to Ozzie Smith to Lou Brock to Stan Musial to Johnny Mize to Frankie Frisch to Rogers Hornsby. There is a slight gap when Mark McGwire played and if the steroid dominoes fall, McGwire should also make it eventually.
Yadier Molina is the currently likely Hall of Famer and whether or not you agree with his case, he probably has nothing left to do.