No, it's the FTC doesn't have the authority - this is an easy thing to do federally, just convince congress to ban them... most things should not be decided by the executive.
> Under this Act, the Commission is empowered, among other things, to (a) prevent unfair methods of competition, and unfair or deceptive acts or practices in or affecting commerce; (b) seek monetary redress and other relief for conduct injurious to consumers; (c) prescribe trade regulation rules defining with specificity acts or practices that are unfair or deceptive, and establishing requirements designed to prevent such acts or practices; (d) conduct investigations relating to the organization, business, practices, and management of entities engaged in commerce; and (e) make reports and legislative recommendations to Congress.
It's hard to see non-competes as anything other than an "unfair method of competition", and it's shameful it has taken this long to act.