That analogy doesn't apply. Towards the middle part of the decade the Braves were showing a lot of signs of slowing down, and by 2006, it had finally happened. On the other hand, there is no real reason to think that the Yankees' aren't going to remain extremely competitive in the future.
Now, if the player values winning, I'm not saying they wouldn't choose the Red Sox over the Yankees, for example. What I am saying is if winning is a priority, the Yankees are going to be one of the teams that the player is going to look at.
I'm not going to give you that crap about coming to the Yankees because of the history and tradition. Same thing with the fans. We both know that is garbage, and if it does matter to a particular player, it is likely a small factor.
I'm also not going to tell you that money isn't the most important factor. For the majority of players, it absolutely is. However, I do think that you're minimizing the importance of winning. Money matters to everyone, and winning doesn't, but I'm of the opinion that winning is important to a significant portion of the players. Think of about this: in the mind's of some people, Alex Rodriguez exemplifies the greedy ballplayer. But, to anyone that has any knowledge of the situation, we both know that winning is right up there for A-Rod. He has proven this through his actions.
Here's my other problem with your argument, J_E. You're speaking about the motives of these players as if you know for certain. At the end of the day, it's total conjecture on your part, and, by your posts, you don't seem to recognize this.