Yes, and of course, this should be decided by the Supreme Court - a group of unelected political appointees with no term limits whose sole authority to decide the meaning of the constitution comes from a court case in which they just granted themselves that power[0].
As for having Congress decide every bit of administrative policy, we've been there. It resulted in Congress wasting its time playing cat-and-mouse games with monied interests. They'd pass a bill banning, say, a certain deceptive trade practice; the people doing that practice would maliciously comply with the law[1] and come up with a new way to do exactly the same thing; and the courts would run interference on legal challenges until Congress updated the law to clearly and unambiguously ban the workaround. Or the courts would squint really hard at antitrust laws and say "Oh, uh, funny story, Congress didn't mean to ban monopolies, they really meant to ban trade unions. Those jokers just don't know how to write laws."
Administrative rulemaking was Congress's way to short-circuit the courts ignoring clear legislative intent. If you think "do what I mean, not what I drafted" is a violation of separation-of-powers, I will counterargue that so is the entire concept of common law. In the US, higher courts don't just have the ability to overturn specific cases; their rulings also create precedent that lower courts are bound by. This is effectively a legislative power, being exercised by political appointees!
The worst president I can think of so far has been Donald Trump. I absolutely do not want him having power. However, binding administrative agencies' hands to Congress's whims will not fix that problem. Remember: this is a Congress that, by SCOTUS's own hand[2], has been turned into a political donation mill that occasionally moonlights as a legislative body. The cat-and-mouse game will run far slower with Congress being bribed by corporations to just conveniently forget to close those loopholes. And we don't even get an improvement on liberty for anyone else. There are plenty of ways in which the Presidency can absolutely roadkill you personally, without needing to invoke an administrative body with rulemaking authority.
[0] https://en.wikipedia.org/wiki/Marbury_v._Madison
[1] See also: Apple's response to the Digital Markets Act
[2] https://en.wikipedia.org/wiki/McCutcheon_v._FEC