If the P5 champs get automatic bids, Notre Dame is effectively a G5 schools. Under this scenario, the P5 schools have a tremendous advantage over Notre Dame. Right off the bat, every P5 school would have access to 4 playoff spots, whereas Notre Dame would only have 3. Then, they have practical advantages. P5 schools don't have to compete with the entire nation for the automatic bid, only the other schools in their own conference. They wouldn't have to worry about ranking, strength of schedule, impressing the committee, etc. The would completely control their own destinies, and it would all be contained within the lines of the field. Schools like North Carolina or Washington St would have much better shot at making the playoffs than Notre Dame. For example, North Carolina could make the playoffs simply by winning the Coastal division (not the most difficult thing to do), and then just luck up one time against Clemson or Florida St in the CCG. They could be 9-3 or 8-4 and still make it to the playoffs. Plus, they have the backup of getting an at-large bid if they don't win the conference. That's a huge recruiting advantage P5 schools would have against Notre Dame, should that format ever be adopted.
Sorry, what "you know" from Notre Dame's time in the Big East is not a "fact." It's an opinion, and an ill-informed one at that.