Notre Dame has far and away the largest and most far reaching fan base in college athletics. If you'd take polls in just about every area of the country, Notre Dame is one of the most popular teams besides whatever the local schools are. Whether you're in Los Angeles, New York, Dallas or Cincinnati, you're going find a sizable contingent of Irish Faithful present.
A big reason for this is the fact that Notre Dame has always received a lot of national exposure thanks to scheduling. It started with Rockne's Ramblers traveling coast-to-coast facing off against the best teams in college football and continues today. Over the next four years the Irish play in: Washington DC, Philadelphia, New York, North Carolina, Dallas, Los Angeles, Chicago, Utah, Boston, Arizona, Pittsburgh, Oklahoma and even Dublin, Ireland. That's the true definition of national scheduling, with a dash of international.
If the Irish joined the Big Ten, they'd be locked into nine conference games per year. This would completely cripple the flexibility to play diverse schedule that provides the level of national exposure Notre Dame currently enjoys. It would pigeonhole the Irish into staying within the Midwestern region, something they're simply not interested in doing.