"I would bet in real life a very high percentage of players agents enter negotiations with the players current team, and if the team would meet their demands the player would stay, it is just most teams can't offer what the Red Sox and Yankees can pay, but in HBD all teams can.."
Except that we can see how it actually works in the NFL, NBA, NHL, etc. Favre is a Viking. Seau is a Patriot. Shaq is a Cav (his 5th team). King James is out of Cleveland in a year. Even Brady and Manning will probably end their careers somewhere else. But Rivera, Jeter, Posada... they'll all die in pinstripes and be burried in Yankee stadium, because the Yanks can throw money at problems and overpay aging players, etc.
In real life, what happens when all the teams have the same amount of money is that agents get in players' ears and convince them that by hitting the FA market, they can create a bidding war and get a few more bucks. And the player listens.
The point is, guys like Jeter, Rivera, and Posada don't stay with the Yanks because they love the Yanks, or because they love winning. They stay because they get paid. Look what happens when the Marlins win a WS: everyone's gone in 2 years. Because no one wants to give a discount and win. They want a few extra bucks.
That said, I would have no problem making this a factor in deciding between max contracts in favor of the original team.