Bandwidth limits:
Would be nice to specify global and per node up/down bandwidth limits.
Communicate limits to peers.
Monitor actual bandwidth with peers.
Adjust connections accordingly to attain bandwidth goals/limits.

With Lightning Network:
Prepay for bandwidth/data. Continue paying nodes who continue to send new useful data. Potentially pay different amounts for different kinds of data.
Request refunds when a node sends useless/duplicate/invalid/spam data. Discontinue connection w/ nodes that don't refund. Hence LN payment channel network topography becomes somewhat correlated w/ bitcoin node relay network topography.

Should help nodes get better data faster, improve spam/DDoS resiliance. Incentivizes relay of unconfirmed txs and new blocks, when currently there is only a utilitarian marginal self benefit via helping everyone in general.

Maybe relay advertisements of available bandwidth and prices, etc.

To identify network splits:
Nodes could find hash of "nonce + pub key + tip blockhash" beating a difficulty threshold. Sign, broadcast. Prove their existence and connectedness. History can be maintained and monitored for disruption. Could be made part of the messages that advertise available network bandwidth.

Cheers,
Praxeology Guy