If it were so easy, many South American countries would have become as prosperous and democratic as the US since their constitutions were basically copies of the US Constitution. Yet, somehow, it didn't really work.
You can see the same in many former British colonies. If you read their Constitution, you'll see that they're not much different from what you find in any modern democracy. Bill of rights, checks and balances, constitutional protections for both negative and positive rights. They also inherited the common law tradition and much of their legislation is copy-pasted from UK legislation circa 1960. It's so similar in theory that UK-trained lawyers can usually practice with minimum to nil extra training, as most of the legal education is done from UK textbooks and case books anyway.
Yet, in practice, it's quite different. Sure, you have the same theoretical protections, but they do little good when everyone is free to ignore them. It's nice to tell the courts that they have to be independent and fair, but how do you guarantee that?
"They need to adjust their system, institute checks and balances", etc. is all wishful thinking. It's about as useful as telling a developing country that all they need to do is grow. It's true but pretty useless as far as advice goes. The tricky part is knowing how to move from the equilibrium where the law is widely ignored, where formal checks and balances don't work, where the constitution is not worth the paper it's written on, to a better equilibrium. As far as I can tell, no-one has yet found a magic recipe for that because things are usually the way they are for a reason. It's not like bad institutions just spring up at random: they are usually people who have an interest in maintaining the status quo, and we were able to see times and times again that removing whoever happens to be in power doesn't do much to solve the structural problems and can even lead to worse outcomes (Iraq? Libya?).