Do you think any owner would consider relocating New England Patriots or Green Bay Packers? I don't think so. Just like LFC, these clubs have been an integral part of their comunity, the Packers to the point of being owned by 537,460 local stockholders.
The Patriots have moved, they used to be the Boston Patriots and then moved out of town and changed their name. Yes, 50 years ago, but it still happened.
The Cleveland Browns were an integral part of that city and were moved, and were eventually reformed as a new club because the NFL realised the Browns were so important. But nothing was in place to stop the original team moving to Baltimore. Baltimore of course needed a team because the Colts, also an integral part of that city, moved to Indianapolis. The Chargers were an integral part of San Diego, but they moved, to a city that barely even wants them. But LA Chargers sounds better on the billboards eh.
But I wasn't really talking about Liverpool, because I actually care about the broad scope of the game. I'm not in for just the glory nights and some pan European glamour league, I'm in it for loads more than that. Would I expect us to ever move from Liverpool or be called something else, of course not. But if the argument is that we're fine and sod the rest, that isn't for me.
I would very much worry about games being played all over the place, much like the NFL have started to do, where teams would be encouraged to give up home games so that we could have rounds played in Miami, Singapore, Melbourne etc. And I'd worry about teams not in glamourous locations not being invited to compete in your idea. I imagine there would be no place for the Green Bay's of this world in your big city InterCities Fairs Cup on steroids idea. And that's the problem. In attempting to move away from something you deem unfair (and it is unfair, I have no arguments with that) you're seeking to replace it with something that will also be artificial and rigged in favour of location and against leagues that have more big clubs (4 per country, etc). It would create different issues, and unlike issues people have with stuff that is 120 years old and at least has tradition and tribalism involved, we'd end up having issues with stuff that has nothing behind it and nothing of note that people would wish to save.