I don't think this has anything to do with the Serie A or any other domestic association. The Super League is a mid-week tournament challenging the UCL, domestic leagues are pressed by UEFA to act like this new competition is actually damaging. TV revenues for domestic leagues are still in place, and in fact, the smaller teams could renegotiate to get more money out of the TV deal. The gap between the elite clubs and others will get bigger, yes, but that doesn't mean the smaller clubs are going bankrupt or even get hit financially, it's just a case where the big clubs will become richer.
The way I see it, and I could be wrong, Its a battle between the elite clubs and UEFA. League associations are threatened by UEFA to take a stand against it or otherwise risk getting no financial aid from UEFA and they have nothing to lose. Just oppose and see who wins at the end. Either way, 80-90% of their financial income is secured by TV rights for their domestic leagues not UEFA.
The second bolded sentence contradicts the first one.
Right now there is too big of a gap between the top 3 and the rest, financially. Yet the fact that qualifying to EL/CL can boost a smaller club significantly promotes competition. If we remove this then you freeze the situation and there will be no possible competition from the smaller clubs. Juve, Inter, and Milan will get a guaranteed huge paycheck regardless of what happens in Serie A, and they will be forever increasing the gap with the rest.
So Atalanta is well managed, builds for years with a good project, qualifies for CL, gets more revenue, increases its squad quality, can qualify for CL again, beats Juve, Roma, Lazio, Napoli in league position, is able to start climbing from the provincial small club to a heavy hitter... Now? none of that. Atalanta can place ahead of Juve and Milan in Serie A yet they won't be in the super league, Juve and Milan will get huge amounts of money anyway to "correct" that situation and come back stronger every season.
Clubs outside of the super league are doomed to this situation. Its the worst version of the current EL/CL system because the super league is a closed competition for its founders.
In the long run this creates two very distinct classes and the appeal of domestic leagues and CL/EL will decrease in the face of the super league. And if the appeal of the existing competitions decreases then so will their budgets.