The SEC has gone the longest with divisions (first started in 1992!) I'm sure there are SEC fans that don't remember annually playing non divisional games. The really old SEC fans might remember pre 1992 when SEC teams played each other more often. The younger SEC fans know about the SEC but SEC East teams only think of SEC East teams as annual rivals and SEC West teams as annual rivals. If you're an Alabama fan in your 20's or 30's, the Mississippi schools are annual rivals, Georgia and Florida aren't. If you're a Georgia fan, Vanderbilt and Kentucky are annual rivals, Alabama and LSU aren't. So maybe Alabama and Georgia are used to not playing each other in the regular season anymore.

Meanwhile the Big 10 didn't have divisions until Nebraska joined and had 11 teams as late as 2010. Even after Penn State joined the Big Ten, Illinois only didn't play Ohio State in 2003 and 2004 until they went to East/West divisions (and they played three times in four years 2014-2017). I doubt we're where the SEC is and I wouldn't consider the Western Division teams more rivals than Eastern Division teams of Illinois like SEC teams might now (their divisions are now approaching 30 years).