The 1st class mail monopoly is one that FedEx, UPS etc don’t really want anything to deal with. Personally I would let the private carriers take over everything right down to the local post office. (Have them deliver to the local offices and let the locals deal with it from there)
I was talking to the UPS driver a couple weeks ago at the post office and he pointed out that I can send a letter anywhere in the USA for 46 cents flat (with 20 cents per additional ounce). If I send the same letter through UPS its going to cost me at least $10 and possibly considerably more depending on “zones” and rates.
The other problem is that there are lots of places in the US where the post office won't deliver 1st class mail, at any price, but UPS, Fedex (or even Deutsche Post) will deliver packages.