If it were possible to prevent fraud with very good certainty, I don't think it'd be that bad of an idea. It would save a lot of money if a person wouldn't have to run a re-election campaign at the end of a set term if the person would have obviously been re-elected.
Petitions aren't secret ( you have to out your name on them) so a bad ass government could make things hard for the signatories.
That's also true in the current system. The old Chicago Machine was notorious for getting back at anyone who signed a petition to place any candidate but their own on the ballot.
