NHL is no longer a major sport, NBA has the same issue but its not nearly as bad as MLB. If a free agent hits the market and he is elite how mnay teams in baseball have a legit shot at him? 4-5 teams tops... That is an issue.
MLB deserves more of the heat because fewer teams have a crack at top players. In the NBA most of the true top players will be able to get max contracts from their current team if they want to offer it.
The NHL is major enough to mention. It's also a sport without a salary cap.
In terms of Sabathia, the following teams were mentioned as destinations: Yankees, Red Sox, Angels, Dodgers, Giants, Brewers
I mean, is he going to get an offer from a bad team, who is likely not one of the bigger money teams? Of course not.
The Yanks, Red Sox, Nationals, Orioles and Angels have all been mentioned in the Mark Teixeira sweepstakes. That's right, the Nats and Orioles (because Teixeira is from the Maryland area).
The teams who don't go after the big market guys choose not to do so, either because certain players don't fit their respective needs or there are cheaper, possibly better, options available. They pocket money from the revenue sharing instead of re-investing it in their teams. Now, it isn't enough to land a mega free agent like a Sabathia or Teixeira, but there are solid free agents still about (it happens every year).
Winning = more people to the park = more revenue for the owner -- in most cases
If these teams do like the Rays have done and draft well and
not overpay/invest in borderline free agents (see the Dodgers with guys like Pierre, Jones and Schmidt as examples), teams can be successful.
I mean, the Yanks last won the World Series in 2000, when
their payroll was $107M. It went up five consecutive years, down for two and back up to an all-time high of $209M. They have won exactly zero championships in that time. However, they continued to win, which kept fans coming to the park. And having their own TV network doesn't hurt, either.
Bottom line is, teams don't have to have $100+ million payrolls and sign all the top free agents to be competitive. Look at Oakland, Tampa, Cleveland, Minnesota, Florida, St. Louis, Arizona, San Diego, Houston, etc. All these teams have been to their respective League Championship Series at least once since 2003; four have been to the World Series and two have won it.
It's not all about money. It comes down to good scouting, smart drafting and smart free agent decision.