Don't forgoet that the monopoly comes at the cost that they are required to keep a lot of post offices open in rural areas, which is a very unprofitable enterprise.
Couldn't the government just directly build and manage post offices in such rural areas, and stay out of the postal business in more populous regions? If the problem is insufficient postal services in some regions, it makes more sense to just fund postal services in those regions than to place a blanket ban on postal competition across the whole nation.
But then the government would be operating the rural postal service at a pure loss, rather than using the profitable parts of the postal service to fund the unprofitable parts. That would mean higher taxation with no extra benefits.
There'd be the huge extra benefit of dramatically cheaper postal services for people in metropolitan areas, due to competition. The 'profitable' parts of the postal service are profitable because of its status as a monopoly, and represent a deadweight loss to consumers. If rural post was funded by taxation, at least the burden would be distributed more fairly, instead of primarily upon people using metropolitan postal services.