How would this be enforced? Lockable bins with a key provided for a small fee? Remove the bins from some rows?? Boarding is already chaotic enough (particularly on US domestic flights) without luckless cabin crew having to tell passengers "you can't put that bag there".
Perhaps what they really mean is that if you're travelling cheapskate class you can only have hand luggage small enough to fit underneath the seat, but (again) enforcement would seem tricky ...