I don't think it would for this specific proposal. The FCC's justification for this rule is that insecure IoT devices "could be manipulated to generate and emit RF energy to cause harmful interference". That's why they have jurisdiction here, because they regulate radio frequency use.
This makes sense to me. The definition is slightly awkward, but awkward in a way that preserves the FCC's ability to regulate the issue at all. If you clean up the definition, you can get to a more coherent definition of IoT device, but without the FCC's ability to regulate the devices.
I think the broader definition would probably just fall back to the FTC, and as far as consumer protection goes I think they've been asleep at the switch for decades.
