How much time do you have? lol
The flaws in the Les Paul are what make it so perfect, what make it sound so good and why people put up with it. Think of all the other single cut guitars you can get, PRS and ESP are the first that jump to mind but there are dozens I'm sure.
All of these alternatives fixed the flaws, but they lost what made the Les Paul so amazing, they don't sound quite the same and they don't feel quite the same, they are much better on paper, but when you actually play one they lose the magic that makes the Les Paul the Les Paul.
Sorry I tend to get a bit romantic about Les Pauls....
EDIT: For the record I am not trashing other singlecut alternatives at all, just saying they are different.