What do you think of David Chaum's xx? Each transaction only sent to end charged by a random pool of 5 nodes that reshuffles every 10 seconds. Throughput scales linearly with network size.

Yes, it is a good step forward.

Really, what you need is a distributed hash table (like MaidSAFE), or randomness beacons (like Algorand) to select a subset of the network. This paper shows mathematically that the probability of a double-spend goes down exponentially with the number of notaries, and having the entire network secure every transaction, no matter the size, is wayyyy overkill:

https://arxiv.org/pdf/0802.0832v1.pdf