There is more in play with mail-in voting than giving a particular candidate an advantage in this election. If things go smoothly with no verifiable fraud to point to it only makes sense to expand on the concept. Making it possible to cast a vote from the comfort of one's living room could spell the end of the GOP as it now exists.
Placing such a neutral party in charge of distributing and collecting ballots could end the practice of gerrymandering districts, as most district boundaries now in effect would be shown to make little sense from a voter's perspective. The GOP doesn't even hide its purpose behind many of the ridiculous district lines currently responsible for much of its power but few voters are aware of how the practice favors rural states and districts by diluting the population of metro areas into surrounding areas.
The USPS would be the natural choice of authority to manage such critical factors if it proves it can effectively and efficiently deliver a fraud-free election and make it easier to participate in our democratic process. Both government and business currently rely on the agency to deliver payments and contracts that are critical to our economy, so presenting it as a potential source of fraud is unlikely to gain much traction outside of the minority of true believers and conspiracy nuts.