Users paying relays directly goes against decentralization.
I am not sure about aut-ct; would't a proof of utxo ownership cease to be valid once you do not own the utxo? also, how do you do rate limiting with that?
Discussion
Against decentralization? Not sure why; you choose to use specific relays already, right. If pay is cheap and low friction, don't see a problem there.
(Re: Utxo ownership, it can be snapshot based and size,age filtered. It protects against bursty traffic (so imo rate limiting is the only thing it works well for!) but such tokens can be created in large numbers at low cost so in many use cases they don't fit very well even though they are very private. Hence e.g. ecash paid with an ln deposit.)
Re centralization: If you choose to pay relay A and not relay B, then why would relay B accept your posts? I am assuming they would not; otherwise, relay A can easily spam relay B (if relays compete for payments, then they have an incentive to take down competition, and spam is a way to achieve that).
Hmm, an interesting perspective. First, to be clear, most of these proposals are "self-verifying" so to speak, so the question doesn't arise (i.e. proof of burn, proof of work and aut-ct). Specifically for a payment though, like ecash, I imagined it as "user has N entry point relays, relays talk to each other" and the latter is a matter of relationship between relays. I suspect that's how it works today. Relay X just blocks relay Y when it sees it sending a bunch of objectionable spam, otherwise they choose to cooperate. As for relays behaving adversarially because they might be in economic competition, that could be a good point, I'm not sure.