Kim Kardashian's celebrity can not simply be attributed to her massive wealth, because it was a scandal that pushed her into the limelight in the first place. After her illegal sex tape was distributed, Kim became infamous for that tape alone, not because of her money. The bedrock of Kim Kardashian's star quality is an old scandal and not her wealth.
Kim Kardashian's celebrity always had the potential to become what it has today, but not because of money, only since her father's own fame increased with the O.J. Simpson murder trial. When Robert Kardashian defended O.J. Simpson in court, as his primary defense lawyer, the whole Kardashian family quickly shot to fame. So Kim's fame today is nothing new since her family had held the spotlight before, and that fame is not remotely related to money but rather courtroom drama.