Kademlia could certainly be a part of a solution to this, but it's a long road from the algorithm to the binary that you can start on a bunch of machines to get the service, e.g. something like SeaweedFS.
BitTorrent might actually be the closest thing we have to this, but it is at the opposite spectrum of the latency -distributed axis.
It's a distributed hash table where the value mapped to a hash is immutable after it is STOREd (at least in the implementations that I know)