Another option I was thinking of would be a pretty inflationary (or demurrage) cryptocurrency in which you have some sort of RandomX or other CPU-bound PoW. A web server could act as a mining pool and use mining shares interchangibly with micropayments.
You could do this mining-share method with Monero right now, it's just that you have higher transaction size in Monero and no real analogue to Bitcoin's LN-based microtransactions. Also you would want the cryptocurrency to be more inflationary (or demurrage-based) to promote usage.
Monero's FCMP++ lays some groundwork for payment channels, but it still lacks the nessisary timelocks. Also there was DLSAG which could have enabled payment channels I think, but it's no longer relevant. I also insist that you would need to change the tokenomics to favor greater inflation (maybe you could make coinbase scale linearly with hashrate?), otherwise the miner reward would be economicially insufficient.
1) it requires you to open a lightning channel. So you need some amount of initial investment (which usually means you need a credit card and an account on a bitcoin exchange), not just any computer which is the issue that using mining shares solves. The initial investment is my main grudge, as it is way too much friction for 402 Payment Required applications. Also as bitcoiners like sztorc note, this isn't feasible for most of the world's population due to bitcoin's small block size.
2) It's not private. People are going to be linking these things to their identities on crypto exchanges. So now feds can basicially track everything you do on the internet that way. LN is only private in the sense that not every transaction is broadcast to everyone else on the network, which is a very low bar. Chainalysis is possible with the right connections.
To a lesser extent, 3) Centralization in the lightning routing protocol which contributes to the effect of #2.
2) it is at least as private as cash. If you withdraw cash from an ATM, the serial numbers are linked to your account. But you can simply spend that cash and obtain it from people you know and transact with, in which case it is private. So yes, if you acquire lightning from an exchange, it is not private. But those lightning transfers you receive outside from an exchance, are untraceable and private. And where you send/spend them too is always private and untraceable.
I am not opening libertierian and freedom-of-money discussions, it is all about being able to facilitate micropayments over the internet. In contrast to traditional banking and credit cards, lightning serves that purpose quite well because it is decentralized because it is based on bitcoin.
Re audience, the audience for Gentoo bugzilla went just to zero. If even 1% of the current bugzilla users would use the micropayments, that's literally infinitely more organic human visitors than today.