Ordering a new election from scratch and obtaining an air of legitimacy requires either that the rules for that were written ahead of time, or that the winner of the disputed election ask for the new election.

In the US, I haven't seen any indication we have rules for a new election. We certainly don't have such rules for the president, except that the electors can be selected by state legislators and if the electors don't provide a result, US legislators can select the president.