I did provide a example:

> You get a lease for a /N+K address. /N routes to your router which routes the last K bits just like normal as if it had a /N-M to a /N route.

> This still sounds like a very bad mixing of layers, even if done in a perfectly standardized and uniform way.

No, I am describing a generalization of IP to arbitrary concatenated routing prefixs.

NAT has the same problems as if we lived in a alternate world where we decomposed IPv4 into 4 8-bit layers and then used a different protocol for each layer. That is obviously stupid because the subdivision of a /8 into /16s and a /16 into /24s is fractally similar. You can just use the same protocol 4 times. Or even better, use one protocol (i.e IP) that just handles arbitrary subdivision.

In the IPv4 (no NAT) world your application has a 49-bit address. Your router is running a DHCPv4 server and allocates your computer a /32 and your computer is “running” a DHCPvPort server that allocates a 17-bit prefix to your applications.

In the IPv4+NAT world your application has a 49-bit address. Your router is “running” a DHCPv4+Port server and allocates your applications a /49, but only tells them their /32 and then rewrites the packets because the applications do not know their address because the stupid router did not tell them.

In good world your application has a 49-bit address. Your router is “running” a DHCPv4+Port server and allocates your applications a /49 and tells them their /32 prefix and 17-bit segment. No packet rewriting is necessary.

Your router could also choose to allocate your computer a /32 subnet and leave DHCPvPort to your computer. Or it could give your computer a /31 if you have 8 interfaces. Or a /34 as a /32 subnet with 2-bit port prefix. Each node routes as much or as little routing prefix as it understands/cares about.

This is a generalization of IP that can handle arbitrary-length, arbitrarily-concatenated routing in a completely uniform manner and all the pieces are basically already there, just over-specialized.