I'm mostly guessing at this because I'm not very familiar with Lightning Network, but I think they'd need to be closed out periodically as well in order to settle up? Plus, I think you'd ideally want an account with each vendor that you deal with, not just one account, otherwise I think the channel would probably need to be managed by some central authority who manages the accounting between you and whoever you're keeping these side accounts with, which seems not great for a number of reasons....and then on top of that there's that 350 million is just one country, let alone the entire planet.

>I'm mostly guessing at this because I'm not very familiar with Lightning Network, but I think they'd need to be closed out periodically as well in order to settle up?

AFAIK they can be kept open indefinitely.

>Plus, I think you'd ideally want an account with each vendor that you deal with, not just one account, otherwise I think the channel would probably need to be managed by some central authority who manages the accounting between you and whoever you're keeping these side accounts with

The whole point of lightning is that you can use the network to route money between nodes, so you could make payments even if you don't have a channel open with the person you want to make payments with. It's not unlike how international wires work. If you bank with a local credit union in country A and you want to wire money to another local credit union in country B, the wire might bounce between multiple "correspondent banks" eg. credit union A -> big bank A -> big bank B -> credit union B.