Human readable to IP: DNS
Private IP to Public IP: NAT
MAC to Private IP: ARP
Public IP to AS: BGP
With a block chain DNS it may be possible to replace all of them with a single protocol, but it may well turn out to be an academic exercise.
That deals with DNS (though how much has it been used?), but what about the layers of the stack?
Most of computing is about mapping A to B and maintaining databases of those mappings :-)
Most of these systems are about naming things and cache invalidation.
I could maybe see a use case for DNS but then either each computer has to have the full blockchain locally or rely on providers to do that for them in which case we're basically at the same model we have now (with root servers and DNS servers).
Obviously you don't want to publish private IPs, etc. to other computers... so inside a local network you're not buying yourself much.
For routing tables I could see more of a use case for blockchain technology since you can actually verify the routing tables and prevent BGP spoofing, etc.