Not usually the top thing on a free agent's mind. Top dollar, playing/living environment, and chance for championships are usually the top 3, in some sort of order.
Being a hero and saving a franchise in trouble aren't usually a big concern, seeing as how baseball is tough to effect that much change on as an individual. Besides, if the difference between playing for a contender and playing for a rebuilding team is a couple million, most players will chase the rings instead. Easier, don't have to carry the load, and you're part of history. Better to be remembered as part of a championship team than part of a team that "started to turn it around" so a team could eventually win later.
Drew Bledsoe saved the Patriots, but Tom Brady is the guy everyone loves...