The only sport that seems to have figured it out is football, with far fewer free agents and far less roster turnover.
The NFL may be the worst for this. The last of HOF caliber players that finished their careers for other teams is very lengthy. Montana, Manning, Favre, Rice, Dorsett, Unitas, Namath, Franco Harris, Alan Page, Cris Carter, OJ Simpson, Emmitt Smith, Earl Cambell, Thurman Thomas, etc, etc.