> UPS and FedEx only offer delivery to these locations because they see it as a required feature to remain competitive with USPS.
If it isn't profitable to offer delivery there then they would have no reason to compete for it even now, and if it is then they would do it regardless.
But more to the point, it's possible that in a competitive market there would be different optimal solutions. In a very rural area, rather than sending a mail truck on a fifty mile trek through the wilderness to deliver one parcel, everyone in the area might have a mailbox in the town center and pick up their mail whenever they go into town, because that would be cheaper by enough that people would choose it over the more inefficient/expensive alternative. You can't justify the entire USPS just to avoid that sort of increase in efficiency.
> If it isn't profitable to offer delivery there then they would have no reason to compete for it even now
Incorrect. They are not competing for that service. Rather they extend their networks to match USPS because they wish to attain feature parity with the USPS. It would be annoying to address a package to a U.S. address, take it into FedEx and find they would not deliver it. This is the case with many smaller parcel carriers. The large national carriers wish to be competitive in cost and convenience to USPS.
You can read about USPS's universal service obligation here.
> In a very rural area, rather than sending a mail truck on a fifty mile trek through the wilderness to deliver one parcel, everyone in the area might have a mailbox in the town center and pick up their mail whenever they go into town,
That is in fact generally how it works but even still the postage rates for rural areas are subsidized by urban areas.
> Rather they extend their networks to match USPS because they wish to attain feature parity with the USPS.
But that doesn't even make sense. If it costs more to ship to a particular address, they have no reason to refuse to do it rather than simply charge an amount that causes it to still be profitable and then turn a profit in doing so.
> This is the case with many smaller parcel carriers.
Presumably because they know they don't have any operations there at all, and so the price they would have to charge wouldn't make them competitive with even FedEx and UPS. That proves nothing about whether the bigger carriers wouldn't still do it when they're positioned to offer the most competitive price.
> That is in fact generally how it works but even still the postage rates for rural areas are subsidized by urban areas.
But why is that a good thing? Cross-subsidies are inefficient. People in urban areas can be just as poor as people in rural areas, especially given the higher cost of living. And if you really want a subsidy like that then make it explicit -- and maybe pay for it on the backs of people who can afford it rather than people who can't.
If it isn't profitable to offer delivery there then they would have no reason to compete for it even now, and if it is then they would do it regardless.
But more to the point, it's possible that in a competitive market there would be different optimal solutions. In a very rural area, rather than sending a mail truck on a fifty mile trek through the wilderness to deliver one parcel, everyone in the area might have a mailbox in the town center and pick up their mail whenever they go into town, because that would be cheaper by enough that people would choose it over the more inefficient/expensive alternative. You can't justify the entire USPS just to avoid that sort of increase in efficiency.