My question is this: Isn't it the case that LN only works well if there are lots of transactions in a channel? That is, if Alice sends 0.00001 BTC to Carol via Bob, and that's the only transaction in that channel in, say, a month, then benefits #2 & #3 above don't really apply since you effectively have a 1-to-1 relationship between a LN transaction and a blockchain transaction. Is that correct?
Well, apart from the fact that LN channel would still be beneficial here if it stays open for 2 months, it still has transitive properties.
When you open a channel with someone, it is not just that you can use LN with them, but with anyone they have an open channel with, as well.
So there is obviously more to it than that.