I think the issue is that the environment you're in often creates the results - and not being an ******* is a pretty low bar. An aging veterin is with a team for a few years, producing on the bench for a very good young team that has success. Maybe he has a lot in common with some of the younger players, he's comfortable in the environment, earns their respect and becomes a great mentor for them. He develops a reputation as being a great veterin.
That veterin becomes a FA and is signed to play a similar role on a new team. However this team isn't nearly as successful, they have a rash of injuries and this veterin is pushed into an extended role where he isn't nearly as successful. It's this first year on the team, he doesn't know anyone that well, doesn't have a lot in common with the younger players on that team and isn't performing on the field. Now he's probably worried about keeping his job in general and probably isn't providing any of the mentorship they thought they'd get from him.
I mean good luck replicating that type of relationship with some old veterin you're bringing in for a year or two. Foolish stuff IMO.