Not on such a widespread basis, no (exceptions exist). For example, Wikipedia lists the Crown Prosecution Service as one such UK government department, but in the US the Attorney General directly governs the Department of Justice. This led to the then-chronic debate about just who had the authority to oversee/direct the Mueller investigation.

Even when an organization is set up outside the traditional Cabinet hierarchy, its leadership is still typically appointed by the President (often with Senate confirmation), such that a new administration should quickly expect to appoint a working majority of directors.

This can also directly cause problems of governance. The Federal Election Commission (https://en.wikipedia.org/wiki/Federal_Election_Commission) is an independent agency that is responsible for administering elections law, but because of Presidental/Senate deadlock the board no longer has a quorum required to take official actions.

Despite their many failings, I actually think this system works pretty well, and I'm always impressed at the reasoning behind supreme court rulings --even those I don't agree with.