I agree with your theory. I just recall when the 2003 shakeup was happening and the idea of a split was just about coming to fruition, Notre Dame was expected to remain with the basketball schools.
Why? All the basics I mentioned such as the northeast markets (again, the largest markets for Notre Dame alumni are New York and Chicago) and the association with similar minded religious and academic schools. Also factor in the lack of pressure to join for all-sports by remaining with the basketball schools since there would be no football. Lastly, what's to say that the football schools even want an non-football member?
I don't think Notre Dame was expected to at all. There was no chance Kevin White moved Notre Dame in with basketball (He came from Tulane and saw what leaving the SEC to be with "like minded academic schools" did for their sports).
The association with schools of "similar budget" is more likely than "similar minded academic and religious."
Academically it doesn't get any better than the Ivy, but you think Notre Dame athletics would join that conference?
It's all about the (1) money and (2) the NCAA championship access. In the long run, leaving Marquette, DePaul and Xavier (catholic, regional rivals) back in the day was worth it because of the exposure the Big East brought.
Their non-revenue programs would lose A LOT from going with the basketball schools. And when you think about it, the basketball league is going to lose a lot too without Syracuse and UConn unless ESPN is behind the conference. If ESPN doesn't promote that league like they do the Big East, it becomes nothing but what the A-10 was from 1995-2001: The second best basketball league in the east coast. Look how their exposure and rep has dwindled.
And the football schools would want Notre Dame for the same reason the Big East wants Notre Dame now. They are Notre freaking Dame. They are rich, competitive in non-revenue sports, and there's a chance it leads to football games on their schedule at some point. They've always held out hope ND would join for football too.