I say no for a couple of reasons but understand the concern. Would it be an advantage particularly with new players to have an easier non conference schedule to prepare for more meaningfull conference games? Sure, many team use the non conference schedule like an extended training camp, getting players used to different rotations, learning the system etc.
But we don't really have that option. Our big games are mostly out of conference, totally different from teams in the power 5 conferences. If we didn't schedule difficult national opponents then we would have a schedule that would be considered very weak for a national contender. The Big East may be as good as any non power 5 conference, but it still is not at that level.
Every year as the conference portion of the schedule approaches we are rated as having near the toughest schedule in the country. Then teams start playing mostly conference games and the schedule difficulty starts going in the opposite direction. Our schedule difficulty starts to fall and most Power 5 conference teams start to rise. We still wind up with a high level of difficulty, but only because of the early very challenging schedule.
I would rather ease into the season and have the big games toward the end not the beginning, but being in the Big East means if we are going to have a schedule as challenging as the top conference teams, we have to do it that way.
My other concern is recruiting. If you are trying for the very top players, which we do every year I think it would be hard to get them if the biggest games on your regular schedule are Villanova, Marquette, Depaul etc., they want the challenge and excitement of games against South Carolina, Notre Dame, Tennessee, Louisville and other top programs. Once again if you want to play those kind of teams, in most cases it needs to be early in the year, just the way it is if you are not in a top 5 conference.