They're not irrelevant because of a massive Catholic brand, great history up to the Lou Holtz era & they still put quality players in the NFL. But they haven't proven to belong in the BCS-CFP era & know matter how controversial this current "era" seems, it's far better than the AP-Coaches period.
So let's be real here, 4 BCS games for ND - let's break them down - as the results clearly prove that overhype and increasingly ancient history continues to sadly mislead perception:
2001: ND 9 Oregon State 41
2006: ND 20 OSU 34
2007: ND 14 LSU 41
2013: ND 14 Al 42
No other team that played in at least 3 BCS games faired as poorly as ND. They got destroyed in all but one of those games - and if you watched the OSU game - you could tell nearly all game the Bucks wouldn't lose. For comparison, VT had an awful BCS record but many of their losses were close, thus respectable & they at least won a game. ND has been the worst performing blue blood in the BCS-CFP era.
ND would actually be in a better place and their future would look brighter if playing a stable conference schedule. They won't give up their USC rivalry, perhaps one more important, high stakes game as well. If they joined any of the p5 conferences except the Pac12, thus holding the USC game, running the conference table would mean a playoff berth - 95% of the time.
ND doesn't seem built to break into the next tier as an independent, esp with the CFP format & they do have brutal academic requirements compared to most football powers. ND also shot themselves in the foot by taking Michigan off the schedule for the future because it won't take long for Harbaugh to bring them back. This past season, Michigan State was not on the schedule as well- though this series will resume shortly. But what a bad time for ND to take MSU off the schedule because Dantonio has the Spartans on the brink of consistent greatness. SOS is therefore at risk unless the ACC can deliver outside of Clemson and FSU. But how often will they play these teams?
Lastly, ND has always depended on national recruiting & they still do well in this department - but until they find a stable conference slate - too much moving around for these kids. Players need stability to improve themselves - conference familiarity yields a range of measurements to potentially find success. People also forget that Indiana, as far as a local base, can't provide enough to them and 2 BIG schools. The Hoosier state, as a whole, prefer their BIG schools.
But honestly, ND deserves their downward spiral. CF has no business honoring independent status anymore, esp with the CFP, which I hoep expand to 8. I could never imagine a professional sports league tailoring to an independent franchise. What hubris & I'm a Catholic with ND alum in my immediate and extended family.