I checked all of the players elected by the BBWAA since 2000, the following have 0 black ink (based on BB Reference's tabulation, see here):How common is it for a Hall of Famer not to have led the league in basically any statistical category (he was first in, like, assists by a 3rd basemen a couple times)?
Mike Piazza (he did lead the league in OPS+ twice but that apparently doesn't count)
Special shout-outs to Carlton Fisk whose only black ink came from leading the league in triples of all things as a rookie, and to Ozzie Smith who acquired his 2 black ink in the strike-shortened 1981 season for leading the league in games played and at bats while slashing .222/.294/.256.
A lot of players had less black ink than you would expect, one that stood out was Chipper Jones whose only black ink came in 2008 when he lead the league in batting average and OBP. He also lead the league in OPS in 2007 but for some reason BB Reference doesn't count that towards black ink.