score:6
Both separation of powers and checks and balances are important and in a way these two concepts contradict each other. The judiciary has to be independent to check the executive, but it must itself be balanced.
There is no country with true or complete judicial independence, not even the five you named. For instance, the judges of the United States Supreme Court are nominated by the President and confirmed by the Senate. No matter how independent they may be afterwards, the two other branches of government have control about who becomes a judge to start with. As recent history shows, this can be a highly partisan process.
There is the habit to see advantages, disadvantages, and justifications of the own legal and political system quite clearly, while getting only distorted views of the rest of the world. That's a reputation many Americans have, fairly or unfairly.
The European states developed as modern democracies because they had the rule of law, administered by a professional civil service and a professional judiciary. Such a judiciary comes in different forms and traditions.
Upvote:0
Many other democracies have no separation of powers and instead a parliamentary system that connects legislative and executive. But I know of none among them where judges are dependent on superior authority to receive their decisions from. The independence of the judiciary is a high value even in those countries, which I personally know from Sweden and Germany.
That question is separate from how the judiciary developed in those countries. In their past, judges served in the name of the king and were not supposed to be independent. It took a long time with occasional backlashes from the absolute monarchy of 17. century to today for judicial independence to develop