As long as there are dreary winters with Midwesterners dreaming of California, the Rose Bowl will continue to be an obsession.
There's also a sense of tradition involved that extends beyond just football. Since it is played on New Year's Day when many of us are at home (i.e., nursing hangovers, nothing's open, too damn cold to go out, etc) with families, it's woven it's way into family tradition as well as football fan tradition. My mother and grandmothers, for example, didn't really care a lick about football but come New Year's Day they were enchanted by the Rose Parade and would inevitably pay at least passing attention to the game too.
There is also some demographics at work. Plenty of people have left the Midwest to live in southern California and Big Ten school have large bases of alumni there. New Orleans and Miami, as just two examples, are certainly fun & warm but they lack the strength of alumni connections and don't quite fit the allure of "California dreaming" either. To someone growing up in Michigan or Ohio, the culture of California appears fresh, modern and creative. Like a version of what the Midwest could be if we had better weather and a little bit more money. In contrast, southern culture doesn't hold the same appeal to the Midwesterner in general. And specific enclaves like New Orleans and Miami are an extra bit too exotic, too Latin, too steamy. They work well as the occasional no-strings-attached flings but the Rose Bowl is the perfect undemanding steady mistress.
Given time, I think well see Nebraska come around to our "obsession" with the Rose Bowl.