If the first Congress's constitutional interpretation in 1789 was correct, then that suggests that many independent agencies might also be unconstitutional, because these independent agencies are exercising executive power. They're enforcing the laws of the United States. The SEC, the FCC, the FTC, these independent agencies are enforcing laws enacted by Congress and are therefore enforcing federal law, they are exercising executive power. Insofar as Congress has insulated the commissioners in these independent agencies from the president's supervision, control, and removal power, that would suggest a violation of Article II, which vests this executive power and the ability to oversee the execution of the laws in the president. The framers conscientiously rejected having a plural executive, multiple presidents, in the Constitution. They rejected a plural executive because they thought that a single executive, a single person at the head of the executive branch, was necessary for energy in the executive, was necessary for the secrecy and dispatch that was required in the executive, and most importantly was necessary for political accountability. When there are plural executives, when there are multiple heads, multiple presidents, it would be very hard to figure out who was responsible for wrongdoing. Today, much of the executive branch of government is actually split among the executive office of the President and other agencies responsible to the President and independent agencies, agencies whose commissioners, whose principal officers, are insulated from the President's removal power, who are insulated from the President's ability to oversee the execution of the laws. This looks very much like the plural executive that the framers explicitly rejected.