You cannot dismantle the only mail service that is OBLIGATED to deliver mail to every address. FEDEX and UPS don't deliver out to my wife's grandmother. FEDEX and UPS don't deliver to my Uncle's factory, in the middle of a medium sized town in north east Texas. But the Post Office does.
When you get rid of a government service that has literally served the entire country, and replace it with a profit driven company, you will disrupt the entire country.
As much as I dislike how crappy the delivery of the USPS has become (I still rely on them for a couple clients who don't believe in digital payments even if I discount their invoice, and my wife's and my prescriptions come through the mail), they have been much more consistent and on time than FEDEX or UPS. I'm actually still waiting on a package via FEDEX that has been out for delivery (in California not NY where I live) for about 3 weeks now.