Interesting numbers, that's for sure.
SEC teams, and particularly Alabama, have had an advantage in bowl appearances as far back as the 1910s and '20s. In those decades, the only bowl was the Rose Bowl, and Alabama appeared in it several times, along with the Pacific Coast teams, of course. Nebraska's conference — first, the Missouri Valley, and then the Big 6 — didn't allow its teams to participate in the Rose Bowl. The 1915 Nebraska squad was invited, but the conference voted it down.
When the Orange, Sugar and Cotton began in the mid-1930s, filling the seats was the most important consideration in each bowl making money. The Cotton hitched itself immediately to the Southwest Conference, guaranteeing its champion a spot. The Sugar Bowl took the SEC champion from the beginning, but it also invited several teams from the SWC in its early years. The Orange Bowl also invited several SEC teams in its early years.
In other words, SEC and SWC teams weren't left begging for post-season opportunities.
At the same time, the Big 6/7, Pac-8 and Big Ten often limited their members to just one bowl per season. In fact, the Pac-8 and Big Ten didn't lift their Rose Bowl-only restrictions until 1975. You probably recall Nebraska earning an Orange Bowl berth after the 1954 season only because the Big 7 didn't allow any team to go to two consecutive bowl games.
Notre Dame self-imposed a bowl restriction between the 1924 Rose Bowl and the 1969 Cotton Bowl, eliminating itself from that list.
Take 1967, for example, when there were 8 major-college bowl games, so 16 slots available. The SEC accounted for 5 of those slots, including 6-3-1 Mississippi and 6-3-1 LSU, who went to the Sugar Bowl with that record. The Big 8 accounted for 2 slots with Oklahoma in the Orange and Colorado in the Bluebonnet. There were 4 independent teams in bowl, and 1 team each from the SWC, the WAC, the ACC, the Big Ten and Pac-8.
Finally, if Oklahoma hadn't put itself on probation so many times over the years, the Sooners would be second on that list. But fish gotta swim, birds gotta fly and Sooners gotta cheat. It's in their DNA.
So, yeah, Nebraska's accomplished quite a bit in its history, and the hot-weather schools in the former Confederate states have always had a built-in advantage. But you already knew that.