There is nothing in the Constitution that explicitly prohibits legislative power being delegated to the executive nor vice versa. The Courts are sorting this out, people are upset, they're tabling stupid suggestions--whatever.
What you're failing to grasp is how those transfers weaken the power and shape it to their vessels. An agency has less rule-making power than the Congress has in legislating. It also exercises it subject to the rules and restrictions of the executive branch. (You can't FOIA the Congress.) Moving Congress's power to the FTC changes that power; the same if you move enforcement to a glorified Congressional committee. Every matter of enforcement would either require a full act of Congress, or, could be endlessly dragged out in the courts until the Congress changes and everything resets. (We aren't on the 109th FTC. We are in the 117th Congress.)
Congress delegating its authority to agencies simply results in a more durable transfer of power than the executive deputizing a committee of Congress.
What about other agencies? The EPA for example? Now environment regulations will be a political game and could change drastically as congress swings right and left.