There is no competition to the DMV, so there is no incentive to run it well.
The USPS will always exist due to being a federally funded service, so there isn't a massive incentive to compete with FedEx, UPS, etc.
Since these organizations do not live in competitive environments there is no drive for them to ever improve.
They cannot be improved with elections because the political state of America is so polarized that it is broken. Elections are decided on one thing alone - whether you run as red or blue. Platform objectives (eg "fix the DMV") are irrelevant because they no longer sway voters. All that matters in an election at this point is whether you are Republican or Democrat.