Well the Yankees had $$$ to resign all three said players, but I'm fairly certain that Jeter and Rivera would be lifelong Yanks even if there had been a salary cap all this time.
I think a salary cap would help the competitive balance of the league (both a maximum and minimum cap), keep draft pick and veteran salaries in check without getting astronomical (A-Rod/Strasburg) and encourage teams to draft well and use their farm systems.
Plus, competitive teams like the Yanks and Sox could still sign vets through a 'mid level exception' like many NBA teams do, so they would still have ways to gain an edge to try and win titles.
Lastly, like Mass states, it would help franchise players and therefore each franchise.
Just look at Hockey: each team has 2-3 big name guys and those that don't are positioned to draft big name guys to remain competitive. Only rarely do franchise guys get traded and when they do it's for equal return and strictly financial reasons. And still many teams remain competitive for years such as the Red Wings, Sharks, Flyers, Canucks and Pens. Even franchises with financial problems like the Sabres and Predators have managed to make the playoffs more than 1/2 the time over the last decade!
There is really little downside unless ownership is truly inept and since salary caps would affect many 'bottom lines', it would stand to reason that terrible owners would lose $$$ and be forced to sell to better ones, which is a huge plus (in theory).
I hope that once Crypt Keeper Selig leaves as commish and new blood wakes up and implements a cap like every other major American Sport already has.