People have pointed out that JR seems to enjoy the "safety" of having his team earn $20-30M of net profit each year. Why risk adding a ton of payroll or investing in a massive expansion of your minor leagues/scouting/international player development when it could implode and hurt your bottom line?
It's easy for JR to set aside his "fan emotions" as owner of the White Sox. The Sox are not his first true baseball love...the Brooklyn Dodgers were. Sure, he wants the Sox to win and be successful, but he won't stretch himself financially to get them to the promised land. To compare, Mike Illich was born and raised in Detroit and has been a lifelong Tigers fan. His love for his boyhood team (and his deep pockets) have caused him to make "irrational" spending decisions by paying huge salaries to the game's top stars (Cabrera, Verlander, Fielder, etc).
Put yourself in JR's shoes: What if you were a super-successful businessman who acquired a baseball team that you had very little emotional connection to (like the Rockies for example). Would you dip into your personal wealth just to make the Rockies great? No, you'd focus on turning a profit year in, year out, and your emotions as a sports fan certainly wouldn't interfere with your business decisions for the team.