I'm trying to understand how Lightning Network will work in practice. As I understand it, there are three benefits: (1) Fast transactions; (2) reduced transaction fees (enabling micro-transactions); and, (3) reduced impact on the blockchain since there are fewer actual blockchain transactions. Please let me know if I'm missing something there.

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?