Only 2 of those 16 franchises that won a World Series though were a small market(Kansas City, St. Louis)
In the NBA Milwaukee, Denver, San Antonio, Cleveland have all won titles in that time period
In the NFL Green Bay, Kansas City, Tampa Bay, New Orleans, Baltimore, Denver & Pittsburgh have all won Superbowls.
In the last 10 years only 1 small market MLB team has won(KC)
In the same time period we've seen Milwaukee, Denver, San Antonio, & Cleveland have won in the NBA meanwhile Kansas City, Tampa Bay, and Denver have won a Superbowl
There might be more "parity" in MLB but it's only among the large/medium markets and doesn't extend to the small market teams like other sports do.