Can you explain why they don't have that authority? Do you think Congress can't delegate its power through a statute? Or do you think that it hasn't done so in this speciifc (Section 5) instance?
The latter. Courts are skeptical of agencies "discovering" new powers decades later that are based on vague sections of their enabling statutes. Congress could of course directly ban non-competes or amend the FTC Act to give the agency this power.
This is hardly a new power, the FTC already regulates business contracts such as franchise agreements. This extends as far as Fortnight’s item shop.
It’s one thing for agencies to suddenly focus on some new area tangential to their mandate, but this seems to be exactly that they are supposed to be looking at.