Indeed. I imagine that if the USPS were to be dissolved, there would need to be federal regulations put on their private competitors requiring universal service

Indeed. I imagine that if the USPS were to be dissolved, there would need to be federal regulations put on their private competitors requiring universal service with low-cost options, much as there are in telecom. (And that the general public would strongly support such regulations not covering "junk mail".) I wonder whether FedEx/UPS/et al would be interested in such a system or not.