Article I, Section 8, Clause 7 of the
United States Constitution
That's it, there is no law about home delivery. It's 100% a courtesy.
You are not paying tax dollars to have mail delivered to you either.
There is a such a thing as a mail delivery manual, but because there is no laws that state that delivery to a home is a right or entitlement so it can be cut at any time.
The fact that there is law like this is how UPS, FEDEX and others can deliver to your home.
The NALC has tried to fight the cutting of mail routes, and establishing of routes for years.
The 3 towns I live near has zero home delivery. If you want your mail, you walk to the post office and get it.