USPS must provide universal service. UPS and FEDEX only provide service where it’s economical to do so.
The USPS first class rates are a deal that would go up immediately if taken over by Fedex or UPS. IMO, the problems are the union and the attitude of the carriers on the street which are intertwined. You could make the USPS over as a true service at your doorstep with a smile.
Of course I’m dreaming.
When I lived in New Hampshire I used to see the UPS truck drop off packages at the post office so the mail carriers could take care of the final delivery. It must have been cheaper for UPS to pay the USPS to do it than to do it themselves. I doubt that is just unique to my one area.