This would solve a few of the big problems we have:
* All sorts of MITM and evil resolver attacks would be prevented.
* Since DNS queries are local, there would no longer be a privacy concern with resolving a name.
* Even if the P2P network mechanism were to be blocked, since every host connected keeps a full record (though not necessarily with history) it can still be distributed via sneakernet.
* DNS updates are as fast as the network is, no longer depending on turtles caching all the way down.
* DNS amplification? That's gone, as resolvers no longer need to query external sources.
As many will quickly notice, we would likely still need remote resolvers for battery constrained devices as this would keep the network interfaces busy.
The one big political issue that would put a stop to this is that this would cause all zones to be world readable. Many people treat zones as something private and to them exposing the zone file is the same as exposing their network. My view is that if it has a publically routable IP then it is already exposed, but not everyone shares my view.