The Constitution of the United States of America was created no just for the majority interest, but also for the minority interest.
The founders cared a lot about not creating too strong of a federal government, but also did not want to create too weak of a federal government as the government had essentially failed under the Articles of Confederation. To prevent a future failure the founders generally erred on the side of caution (stronger government), but put checks in the system to prevent abuse.
The Judicial Branch was not seen as that strong of a branch. It was not given the power to spend money nor to exercise force (technically bailiffs are court officers but this is not much). For example, the U.S. Marshals are an agency of the Executive Branch and are tasked with enforcing the Judicial rulings of the United States; however, this power is checked by the President as they are part of the Executive.
In recognition of this inherent weakness of the Judicial Branch, while at the same time importance of the branch in preserving liberty, Justices and Judges were given lifetime appointment. This allows them to withstand political pressures of the day and remain concerned with interpreting the law in an independent and just manner.
There is also a sense of finality to the Supreme Court. Once an issue is decided it remains the law of the land unless there is a constitutional amendment (not exactly that in practice, but in theory).
The reason something similar to the Italian system was not adopted was because then a sufficiently motivated political alliance would be able to change the judges to their favor in a relatively small amount of time (9 years). The idea in the courts was not to balance the separate branches, but to create an entirely different branch composed from judges chosen by different administrations and in a sense generations.
In the United States this system allows the Justices of the Supreme Court and other courts to remain independent and most importantly issue relatively stable rulings throughout the years.