The British Crown had prevented colonists from appointing their own judges. This issue was addressed in the U.S. Constitution by creating a separation of powers and system of checks and balances.
The British Crown prevented colonists from appointing their own judges in order to avoid abuses of power. Similarly, in the United States, the Judicial Branch does not appoint its own judges for the Supreme Court. The Executive Branch, more specifically, the President is the one who has the power to appoint the Supreme Court justices, court of appeals judges, and district court judges.
Such separation of powers is established in Article I, II and III of the Constitution, where the Legislative, Executive and Judicial branches respectively are outlined. Likewise, the articles holds the so-called "system of checks and balance" whereby all three branches of the government oversees, limit and check each other so no part abuse from its powers and a balance in the government exists.