Although, this is a very intriguing idea at first I have a couple of questions regarding incentives and resources of nodes as well as propagation latency.
In terms of peer sketches. What determines how often a node will update a peer sketch? Are they doing it every time they get a transaction, or right after a peer requests it. If they are doing it every time they get a transaction, the sketch takes more resources. If they do it every time a peer requests an update, sketch creation causes a delay, followed by the delay in determining the difference and than subsequently requesting the deltas. It was expressed that this could be done without a hard fork because it doesn't change the incentives. I think that this does change the incentives of nodes in an indeterministic way which could lead to various forms of selfish and resource optimization behavior especially against small nodes.
The second question I have is how does this net effect latency. The theoretical propagation time of data across the network is actually the upper bound on network throughput. Introducing latency to aggregate, share, compute, request and share transactions likely adds a lot of latency to the network which can actually decrease throughput. Any thoughts on where the use of bandwidth competing with latency is optimal?