To be fair,
Navy/BYU don't count in the "lock them out of big time games" since neither are in an AQ conference.
Purdue and Michigan State supposedly (by most accounts) were willing to sell the Irish game for an annual PAC12 matchup.
Texas (who first off isn't in the B1G or PAC) only has a home and home scheduled with the Irish in 2015/16 and 2 neutral site matchups in 2019(in Texas but TBD DFW/Hou/SA)/2020 (Chicago) and nothing more as of yet (though much has been rumored) but they've only ever played 10 times before these matchups (mostly through bowls) so they also shouldn't be in this conversation...
The enablers are clearly the ACC and USC/Stanford.
For those who want the Irish to join a conference, the other major conferences need to cut the Irish out of the post season conversation and make them communicate through the ACC (thus giving the ACC more control over the Irish and taking away their influence at these meetings).
Then we need to see the PAC12 go to 16, and the ACC to get raided for at least UNC possibly by the SEC meaning they'd be at 16, and with everyone at 16 obviously the B1G will also be expanding so they just need to grab a 15th members (KU/UVA) and offer ND its final chance to join the conference because when all this happens (around 2025 or so) the GOR would have to be up and so will the new bowl/post season agreements. If ND thinks they may be finally getting cut out of the process, then clearly they would have to end their independent streak and join up with either the B1G or the ACC once and for all. But they'll hold onto it until then so I wouldn't expect any changes for at least the next 10 years.
I don't think BYU and Navy's place is overstated in the big picture, though. Both could be major conference members if they wanted to (Navy chooses not to, having avoided the Big East for decades, and BYU runs on a "PAC or bust" philosophy). But, more relevant to Notre Dame: being independents, it resolves scheduling conflicts where they exist when running up against more restrictive conference scheduling (ie: why Notre Dame's Big Ten games are always in the first few weeks of the season, unlike USC, Stanford, Pitt, or BC). Army's just as much of an enabler.
I added Texas because they wanted what Notre Dame got from the ACC, and may still currently desire it. A school like Texas trying to copy the model of Notre Dame is as destructive toward the cause of "reigning in the Irish" as the ACC and the two PAC schools because of the "stroke" Texas has as a national program and within the Big XII (and the Big XII is now a lot more flexible with non-conference scheduling at ten than it was when twelve).
The scheduling issues for indepdents, Notre Dame included, are weeks 6-11, deeper in the conference season. Given a willing crew of various independents, the ACC, and the PAC duo, the Irish really have no reason to budge. With the flexibilities of the Big XII, including their campaign for Notre Dame in an associate membership agreement, I think they, too, can feed into what the Irish desire.
And what about the bowls? Any bowl will probably find a way to fit the Irish in. They're covered in the ACC now, and most believe some of those games the Irish will never see even if 6-6. They just get all the breaks...