The transaction is really instantaneous despite low fee?
Lightning Network requires you to pay regular on-chain fees when opening or closing a payment channel. Every transaction in between -- could be tens, could be thousands -- is handled instantly, without an additional on-chain fee overhead.
Given full blocks, the transaction fees will be more or less the same, but you can handle many more transactions at the price of just two. Think of it as a flat rate.
Assuming that LN will take most of transactions off-chain, blocks will likely be rarely full -- at least for the next few years -- and thus transaction fees as a whole are likely to be reduced as well.
the way i see it, is that LN has the potential to decrease the "load" on the main chain by a lot. for example one of the biggest usages of bitcoin is for speculation (trading so to speak). with LN you could deposit and withdraw your bitcoin to and from exchange for little to no fee and instantly. this can reduce the risk of exchanges scamming to by a lot. it opens up easy and fast arbitrage trading also.
not to mention how it can make decentralized exchanges so much easier. the cross chain exchanges or Atomic Swaps become easier.
and this is a lot of transactions in bitcoin right now and most traders want their money to be active not sitting in a wallet
there are others things like gambling sites, mixers, and a whole lot of services that people use regularly like this.
but at the same time it will never be "all" and as you said we still need to make on-chain transactions. which is why i believe we still need a small block size increase.
