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.