I love this idea. Absolutely love it. If I was running one of these 'big' clubs I'd also pull out of the domestic leagues as well.
I have zero interest in watching my beloved Rossoneri play freakin' Sampdoria, Crotone, ect or some other podunk team from cowtown. Nobody wants to watch the Boston Celtics play the Maine Red Claws, it's the same darn thing.
I guess here in the US we're much more used to closed competitions where the number of teams is fixed irrespective of the results. The NBA will always have 30 teams, they will always play each other. Teams don't get promoted or relegated based on performance. All of the teams in the tournament have the chance to go to the playoffs, we don't have spots reserved for the big market teams.
We also don't really have a Champions League as such, though I guess the closest comparison would be the NCAA basketball tournament where teams are drawn from all conferences across the country based on their performances in their conferences. I guess it would be as if Duke, North Carolina, Kansas, Kentucky, UCLA, Indiana, Louisville, Michigan, Georgetown, and a bunch of other "elite" programs decided to set up their own "Super Conference" and play each other regularly, so that they didn't have to take the risk of missing out on March Madness. They would have some kind of qualifying process to get 5 ring ins a year to make up the numbers, save their best players for that competition, and not take normal conference play seriously because there's no incentive to do so, and either not participate in the NCAA tournament at all, or not qualify because they weren't taking it seriously.
I guess the broadcasters might not like it that much, and neither would other teams like Gonzaga, Baylor, or Villanova, that might be as good as or better than some of those bluebloods, but don't have the cachet or the brand name. And the thrill of seeing a No15 seed Oral Roberts upset a No2 seed Ohio State this year, or No10 Davidson with Steph Curry beating No2 Georgetown in 2010, or or No8 Villanova beating No1 Georgetown in 1985, would be gone.
That's probably the closest analogy to US sports I can think of.