Think how Lightning nodes compete for fees by offering cheap routing fees.
Competitors keeps fees low, but the best node operators can make a decent living from routing payments
Discussion
Yes, I think I can see the correlation. Almost like a bidding pool. Users would set their split, and that would determine the budget for relays, etc.
Users could also favorite certain relays they wanted to always carry their messages.
Yes, new relays could enter the market by offering low fees to start with and then increase them as they build their reputation.
I love this idea.
You could also have an amboss style monitoring system for relays, giving stats for things like uptime, connectivity, fees etc which feeds into the suggestion algorithm.