Executive departments not answerable to the President are unconstitutional, full stop. We do not allow Congress to delegate its authority and/or strip authority from the President and move it into a fourth branch of government.
https://en.wikipedia.org/wiki/Independent_agencies_of_the_Un...
I always find it weird when people make statements like yours, full of confidence that what they are saying is the way everything is and should be, when they are literally completely and utterly wrong. What you have is an opinion of how you think the government should be run, based on your interpretation of the constitution. The reality is that the Supreme Court thinks your interpretation is wrong, and since they're the deciding factor that means your interpretation is wrong.
https://www.npr.org/2020/06/29/884958645/supreme-court-rules...
The non-delegation doctrine exists, but independent agencies survive because its administrators are Presidentially appointed and Congressionally confirmed, and other factors. Other commenters have rightfully also pointed out that you probably have more chance to engage in the democratic process with an independent agency, which also tend to have greater representation from the political party not in control of the Presidency.
It would be correct to say that there are new attacks on the administrative courts systems and extent of deference to administrative rulemaking. But you're wrong about independent agencies.