we have a distinct advantage over almost every other club in the country to an almost comical effect.
The solution to horrendous inequality isn't to buy into a system that exacerbates and takes advantage of that inequality to screw everyone else over.
I'm not saying LFC are going to be some Robin Hood club, and we're always caught between trying to maintain the integrity of the club while competing against rivals owned by Oligarchs and Oil Tycoons but basically turning around to all the other clubs and saying "nah, we're too good for you now" is the worst example of arrogance. We've been back in the CL for two years and suddenly we're too good for the rest of the country.
The other reason this format won't work is that teams, clubs, players like winning. At the moment, players can win domestic titles in England, France, Spain, Portugal, Italy, Netherlands, Germany etc. Leagues, cups etc. A multitude of ways to earn plaudits, medals, to be remembered.
You bung all those clubs in one competition and suddenly you're in a place where every season, only one club out of Bayern, Real, Barce, Juve, City, us, Atletico, United, Arsenal, Chelsea, Ajax, Porto, PSG, Lyon, Napoli etc etc can win a competition every year. You seriously think that all those clubs would take the risk of going years, maybe decades without meaningful silverware?
The system as it is is ideal in that regard. Big clubs all have a shot at two or three domestic competitions every year to keep the fans happy and engaged, whilst competing for one very prestigious competition in Europe as the pinnacle. The risk inherent in the change would be far too great.