No, the USPS is not constitutionally mandated to deliver to your house.
The Post Office Department did not begin delivering mail to city addresses until 1863. Rural Free Delivery did not begin until 1893.
Before free delivery, you went to the Post Office yourself and asked for your mail. ("Caller service" or "General delivery", both of which still exist.)
Since the 1970s, the Postal Service has been delivering to clusterboxes. Grandfathered areas get to keep their individual mailboxes, but new greenfield development must be built with clusterboxes.
If mail volume keeps decreasing, we'll see greater contraction in free delivery. It all depends on how the politics go.
Funny, that's just what the USPS is constitutionally mandated to do (Article I, Section 8, Clause 7).