IP addresses form a hierarchy, which makes it doable.
I fundamentally believe you should run your encryption over the network, and not try to bake it in.
RPKI and BGPSEC do need to happen but we're an eon away from it being a reality.
Incorrect, you might want to read about TLS SNI (Thought exercise; the server has to pass your packets to the correct vhost before decryption).
You might want to Google dTLS (TLS over UDP) and then read some of the dialogue about why it's impractical on the public internet.
Consider further that by moving your presentation layer logic into the network layer, every time you want to introduce a new cipher you'll need to upgrade every network device on the internet. Think how bad the export-grade crypto problem has been, then multiply by the momentum of Tier-1 ISP install base. Instead of making the network less important, you're handcuffing yourself to Verizon.
Again, I’m fairly network-ignorant, but as far as I can see this constitutes an inversion of the current architecture: routers need to be aware of signatures, such that they don’t deliver an invalid packet (bad signature) to a destination. So the logical layer would be the lowest one, and a router that delivers a packet with a bad signature would be considered defunct.
The funny thing about the current architecture, in my view, is that the correct destination of an HTTP TLS packet is hidden (encrypted) inside the application data (“Host: google.com”). So routers rely on IP addresses to figure out where the packet needs to go, while the logical destination is only visible to the receiver once it decrypts the packet.
The idea would be moving this information out of the application data, making it cryptographically sound (public key is destination, not domain name), and making routers aware of it such that they know whether a packet was delivered to the correct destination by whether it responds with a valid signature.