I think Nostr is so disruptive that some entities will want to shut it down. This is when spam will get serious. At that point, relays may have to enforce proof of burn.

"proof of burn" always struck me as a bad idea. Just pay those relays that you are appealing to care about your notes. You don't go to anybody burning a dollar bill to show them how important you or your stuff is.

To be clear, in this context the coins are not burnt, they are sent to the Bitcoin miners. Paying the relays creates very different incentives, that lead to centralization. Indeed, relays have no reason to cooperate or to trust eachother. If you pay relay A to store and relay your notes, relay B has no reason to trust that the payment was real. In addition, if relays compete for users payments, then it becomes in their interest to spam their competitors.

I would expect both things to occur. Web of Trust among relays and inter-relay attacks.