Germany is 4% of America in size. A single US state with decent population density wouldn't need a nationalized system either.

The USPS gets a monopoly because it is required to go everywhere. If a private company doesn't want to go into Michigan it doesn't have to.

Without a monopoly protection USPS goes from being slightly unprofitable to very unprofitable by companies competing only in cheap areas.

Basically USPS needs $0.78 to mail a one ounce letter overall. However it doesn't need that much for you to mail within the same city, it is probably much less than that.

But they do need it if you send a letter across the country.

They could auction off a universal service obligation to willing bidders. No need to run a federal agency with a monopoly for that.

(And everything you explain could also be accomplished by state-run services, no need to involve the federal level.)