I think, Paul, it would be a lot easier to fix your parliamentary system than our mishmash of a government. National referendums would be by far the quickest way to make some sort of improvement. But you right this would be a long way from perfect.
Just one huge problem when our government was formed was that it had to accommodate slavery, and even later amendments to the Constitution didn’t completely fix just that one part of the problem.
Moreover, how silly is it that huge states like Texas and New York have as many Senators as little Delaware and Rhode Island? Really! The political hurdle just to try and fix that ridiculous problem would be virtually impossible.