If these schools never had the huge football programs, yes they would have zero credibility.
Without the notoriety and prestige granted by their athletic programs, no one would respect their academics.
For a recent example, witness the transformation of USC from a joke of a school (academically) to a somewhat respected, some might even say moderately prestigious (!!) university. A transformation which coincided 100% with their successful football program.
The great team builds recognition. It builds respect. You graduated from a school which is a football powerhouse, people respect you. Even if you graduated decades before they rose to football prominence. Even if you never cared about football. People want to be affiliated with success, thus they want to be affiliated with you.
Without the notoriety and prestige granted by their athletic programs, no one would respect their academics.
For a recent example, witness the transformation of USC from a joke of a school (academically) to a somewhat respected, some might even say moderately prestigious (!!) university. A transformation which coincided 100% with their successful football program.
The great team builds recognition. It builds respect. You graduated from a school which is a football powerhouse, people respect you. Even if you graduated decades before they rose to football prominence. Even if you never cared about football. People want to be affiliated with success, thus they want to be affiliated with you.