Someone must have missed Braves, Dodgers, Marlins, Twins, Blue Jays, Reds, Royals, Diamondbacks, White Sox, Angels, Astros, Phillies, Nationals and even the Cubs winning WS championships
Considering that it was usually either the Lakers or Celtics who won the championship in the NBA before the salary cap, the teams you mentioned and the Rockets and Pistons are sure thankful for it.
No mention of the NHL? Since the their salary cap started in 2005, 10 different Stanley Cup Champions.
Getting tired?