I don't think there is any connection between UConn and VCU. UConn is a former and highly respected member of the Big East, with a connection to seven of the current schools. VCU has very little history with any Big East school.

Rutgers was added to the B1G with a terrible football and terrible basketball program. Colorado was added to the PAC-12 with a low football program. Syracuse was struggling when they were invited to the ACC. Realignment is bigger than any one sport. Institutional fit, which helps drive value, has been at the forefront of conferences adding schools.