You would have to amend the constitution in order to disband the Postal Service. The Postal Service is actually constitutionally mandated
Not if you take the Constitution literally.
The Congress shall have Power . . . . .
To establish Post Offices and Post Roads;
In plain English, that means Congress is Permitted to establish Post Offices. Even if it were mandated it could establish no more than 2 post offices, eg in the White House and in the Capitol and fulfill the mandate.