When there is a monopoly, more densely populated areas cross subsidise more sparsely populated areas. If there isn't a monopoly then companies are incentivised to pick and choose whos mail to carry making it more expensive for everyone else.
I don't think empirical data are especially kind to it.
It also ignores the fact that monopolies have no incentive to produce high quality and ever improving product. They tend to get focused on maximize staff comfort over customer satisfaction.
ADDED: IOW, you could have an external taxpayer-supported "rural mail delivery" department that has a charter to deliver a letter for a quarter anywhere in the country rather than providing a subsidy within the system.
It's mostly academic at this point. (And the reality is most private package delivery is fairly universal because there are business advantages to having a fairly complete delivery network even if it's not necessarily the most efficient decision at the micro level.)