So the saintly-and-holy B1G (several sports, notably football and men's basketball) had 11 teams -- and 11 is a prime number -- with no divisions nor pods (and no full round-robin in football) for 20 years...
The Marinatto Big East (basketball) had 17 teams -- and 17 is a prime number -- with no divisions nor pods (nor balanced round robin) for 9 years...
The ACC basketball of 2013-14 had 15 teams, with nod divisions nor pods (nor balanced round robin); this configuration shall continue unless/until conference realignment.
While a "balanced round robin" among 6+ teams (current NCAA rules) seems most "fair", the whole point of the "conference championship game deregulation" is that rule could be eliminated, and conferences could schedule and align as they choose. For eons prior to "divisions" within major collegiate athletics, many conferences did NOT play full round robin schedules in football, and there were no "pods"...
If "conference championship game deregulation" passes, I see no reason why ACC (full-membership for ND? add only UConn?) and/or B1G (add UConn) would not be perfectly content with 15 members. (If any conference had 15 members, they could each play 8 conference games, consisting of 2 "annual rivals" and then rotate the other 6 games versus the other 12 members, thus playing everyone in conference over two seasons. While this concept is perhaps most easily implemented with 5 pods of 3 teams apiece, I am highly confident that the "rivalries" need not constitute full round-robins within pods... I am just not going to do a mathematical proof at this time...)