the problem with lightning is:
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.