If an executive agency can have legislative powers, then a legislative agency can also have executive powers.
Sure. This isn't a hot take. The legislature can order the executive to take specific actions. It does so all the time. The reason every society in history separates or delineates its executive functions is because many tasks of government require faster action than a deliberative body can continuously commit to.
Congress (big and slow) granting agencies (small and faster) limited rule-making powers increases the agencies' power. The executive granting the Congress limited executive powers (e.g. prosecuting contempt of Congress) doesn't confer an equal power transfer. The executive branch of any system is built to amplify and focus power; the legislature, to distribute it. That executive power, if vested in the Congress, would dissolve across the body.
An FTC under the Congress would have the same authority as any Congressional subcommittee: infinite in theory, but relatively toothless in practice.
Because its every action would be subject to Congressional rules and procedure. It's part of the Congress. That's what putting it under the legislature means.
> why does the FTC need to act so quickly?
Injunctions? Compelling testimony? Conducting investigations? You're confusing Congress with a sovereign Parliament.
No, they can't. Congress isn't sovereign, but it isn't bound by any prior Congress. You could create an exception to parliamentary procedure for the agency, like we do for e.g. CBO, a legislative agency, but it wouldn't be able to actually do anything.
> the same manner that the current FTC does not need to ask for presidential approval
The FTC was created as an independent agency by the FTCA of 1914. A law passed by the Congress and signed by the President. It exercises Article II powers freely and limited Article I rule-making powers delegated to it by the Congress.
When the FTC takes executive action, it does so as an independent agency. When it invokes its rule-making authority, it's subject to all manner of checks and balances, from the President through the courts all the way to the Congress. Inverting that makes the agency useless. It would have rule-making authority similar to the Congress (i.e. subject to full passage and Presidential veto) but none of the executive powers.
I'll admit, this is one of the more creative ways of de-fanging an unpopular agency that I've seen. (I still can't tell if it's parody criticism of Chevron.)
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.
I believe you are misunderstanding the potential change the Supreme Court ruling could have. Each regulation would have to be approved by congress, not appointments.