There is not a single reason on God's green earth to root for Notre Dame. I'm struggling to come up with a reason someone else might come up with for me to refute.
They aren't part of Hockey East (no, they're not [again, no, they are not]). They aren't even East. Hell, they barely even Hockey. They conned the commissioner of our league into letting them join while keeping their own precious TV deal when all the other conferences told them to pound sand. Now that they're finding that everyone else in the conference refuses to kiss the Ass Of Arrogance just because they're the team in the cornfield, they're taking their proverbial ball and going "home," to the Big Ten and its significantly easier competition.
This is good! Swapping out the University of Notre Dame for Lennay Kekua State makes for a far better conference.
Do you like rooting for the underdog and want to see another 4 seed win the title? Please. Notre Dame probably hates being called the underdog (I'm surprised they even accepted an invite to the Frozen Four as such a low-ranked seed), but as enjoyable as it is to think of them as this petulant little anklebiter, let's not pretend this team is an "underdog." They have donations out the ass, they play in a brand-new arena... no, this is a team that somehow manages to underachieve despite its unending stream of resources, not one finding itself punching above its weight.
Do you like the colors blue and gold? No one gives a shit.
Beyond that, there is no reason anyone could have to root for Notre Dame. If you're thinking of doing it anyway, just don't. For once in your life, try to not be an asshole.