The US equivalent to Ofcom is the FCC, which is not as powerful in statutory authority nor as aggressive in practice. Ofcom, among other things, regulates rates and service days for Royal Mail. I do not believe FedEx or UPS would accept this degree of regulation in exchange for the liberty to deliver letters to mailboxes.

What's also significant is that Royal Mail privatization is less than a decade old. From a policy perspective, it's still an experiment. It doesn't actually have any competition for letter delivery. That Royal Mail has survived despite the lack of a statutory monopoly does not mean that the same would be true of USPS.