The SCOTUS likes to decide things on the narrowest possible grounds. That means that if it wanted to reverse this rule it would want to find grounds relating to (3), which as you note it probably could not.
The court could still decide that this rule is a "major powers question" and so belongs to Congress. This would allow the court to not have to reach any question of whether the FTC has broad powers, whether the act that created the FTC is constitutional, or whether Wickard was correctly decided. Therefore it seems more likely that the court would do that -again, if it wanted to reverse the FTC here- than anything else.
Can you imagine if the court ruled the FTC to be unconstitutionally created? They wouldn't risk that chaos.
Congress established many parts of the executive branch. Nevertheless they remain part of the executive branch, a separate branch of government from Congress, and this distinction is legally important.
1. Whether Congress can ban noncompetes nationwide through its ability to regulate interstate commerce.
2. Whether Congress can say "so-and-so can make any laws he wants about x".
3. Whether this is in scope of the FTC's mission of preventing unfair trade practices.
To me, #1 is a clear no for intrastate agreements, but under Wickard it is constitutional.
#2 is yes under Chevron.
#3 seems an obvious yes.
The only question would be if SCOTUS decides now is the time to correct what it sees as prior incorrect decisions.