institution followed by a church institution. Forgive me if I'm wrong, but that seemed a lot like a Jay Hill comment. Maybe my interpretation of context was wrong.
As for qualification for pensions, qualification usually required significant years of tenure in the system. Coaches will not usually qualify because they won't last long enough for the program to vest.
Furthermore, most states are moving away from pensions because they are a terrible idea for public (or private) institutions. 401k and 403b are the primary retirement accounts that are likely available to coaches, just like they are to the rest of us.