Start with having nearly 100% of the games on national TV, even games against low level opponents. The ratings might be pedestrian now thanks to years of mediocre performance; but imagine the attention the program will get if it returns to prominence. It will get more exposure than any other program, and the gap to the next most exposure will be large.
Notre Dame's fan base is incredible. When we talk about soft demand for tickets coming off of a 4-8 season, we mean more than 70,000 tickets sold. Most successful coaches would kill to get the turnout ND gets for every home game.
Notre Dame might not spend on football like Texas does, but it has a substantial budget at the coach's disposal. ND has good football facilities for all aspects of a football player's preparation - physical development, meetings and video review, and even the stadium despite the weirdness of the Crossroads buildings.
Most recruits' parents love the idea of their kids getting a Notre Dame degree for free; and most like the idea of tight reins from a disciplinary standpoint. As long as they think Junior's football experience will be good and they can count on his athletic development, they will be recruiting assets.
Academics are a restriction, but they are more of a restriction for basketball than football because Catholic high schools and suburban high schools with college prep academic programs produce a higher percentage of top football players than they do top basketball players. If a coach wants players who expect to major in eligibility, Notre Dame will not be desirable; but some coaches might like the idea of coaching generally smarter players because he won't be restricted to remedial game plans. Academics can be a positive as well as a restriction.
The job pays pretty well; and if a coach does fail, it appears that he can count on being paid well for years after he's gone. A successful ND coach has countless opportunities to supplement his salary if he's likable.
It's an excellent job. It's hard work, but it's hard work with advantages that few other schools have to offer.