Then miners can spam relays for almost free? 🤷 Miners could sell that capability ...

Anyway, I'm sure you can do better. Use Cashu to reward the first m of n relay operators in a transparent way. I assume, mints can execute arbitrarily complex logic so it should be no problem to have a way to reward the first 5 of enumerated 15 relays for picking up a note. People would have to track if the relays take the money but delete the reward or if they retain the event for a reasonable amount of time but this way at least the relays would get directly rewarded for building the infrastructure.

To avoid centralization, we would need ways to spread the load, favoring less central relays but with the outbox model, people already can use their own relays and have little benefit of using centralized ones.