If we're talking World Series successful, only Frank Chance (Chicago Orphans). If we're talking the team actually was competitive at some points: Lou Piniella (Baltimore Orioles), Dusty Baker (Atlanta Braves), Don Baylor (Baltimore Orioles), Don Zimmer (Brooklyn Dodgers), and Jim Fray (O's/Braves/Brewers/Cardinals). There are probably more I skipped but these are the ones I recall. Still a couple of these I had to look up, I don't pretend to have them memorized.
If we're talking World Series successful, only Frank Chance (Chicago Orphans). If we're talking the team actually was competitive at some points: Lou Piniella (Baltimore Orioles), Dusty Baker (Atlanta Braves), Don Baylor (Baltimore Orioles), Don Zimmer (Brooklyn Dodgers), and Jim Fray (O's/Braves/Brewers/Cardinals). There are probably more I skipped but these are the ones I recall. Still a couple of these I had to look up, I don't pretend to have them memorized.
Lou Pinella played a grand total of 4 games (1 official AB) for the O's. Had a great career with the Royals and Yankees, though.
Don Baylor was successful as a manager? His Cubs winning percentage was .459. He had one winning season and a wild card berth with the Rockies. Overall, he has a terrible record.
The other guys you list, other than Lou, who has won it all with the Reds and had some pretty impressive teams with Seattle (but no postseason success), what kind of success did they have? Don Zimmer had some competitive teams in Boston, but he never won anything. Frey? Overall, after Lou, he's had the most overall success of the guys you list, but he one a division title with the Royals, and one with the Cubs. No Pennants. No World Series.
I don't even understand where you're going with the argument. That former White Sox players haven't succeeded as managers elsewhere? Well, I could make a list of former Sox players that have managed and been successful. Actually, you can make a list of former Cubs players that became managers and became successful. If you meant that a former Sox player was doomed to succeed as a manager of the Cubs, well, I have to agree with you wholeheartedly. But guess what? The reason why that is true is not because former White Sox players couldn't be successful managers of the Cubs. But because former players of ANY TEAM could never be successful managers of the Cubs. QED.
By the way, Elia really only played for 2 season in the big leagues. One year riding the bench with the White Sox. But where did Lee finish his career? You guessed it. The Cubs!
And riddle me this. Has there ever been a manager, particularly since the last time the Cubs have been in the World Series, that has gone on to a successful managerial career AFTER managing the Cubs. The only one I can think of off the top of my head is Joe McCarthy, but that was long before 1945.