Paul Konerko is one of the most revered Chicago White Sox players of all-time, and he should be.  Konerko was the heart of a team that won the 2005 World Series and won the ALCS MVP in the process.  Konerko could hit for power (439 Home Runs), had 2,340 Hits, 1,412 RBIs, and a .486 Slugging Percentage.  

That is the good news.

Konerko’s defense was very poor, as was his speed, and he finished his career with a good (though far from Hall of Fame) bWAR of 27.6.  Still, this is a popular player with a solid career, and he received 2.5% of the vote in 2020.  He may never appear on a Veteran's Committee ballot, but he has a statue erected on the South Side, and in terms of “fame," he had it.