You need to establish each tunnel on chain, as I read it, this requires a commit to the block. So any time you want to open a payment to a 3rd party you need a btc chain transaction. I'm happy to be wrong here, but that's how I read it, and if so then that's not really gonna fix the problem at all; it's just going to make more not-actually-decentralized services.
Maybe it's an okay thing to imagine a world where there is a primary chain for major institutions and then brokers on this chain using lightning. But I gotta confess I was sorta signing up for something more revolutionary than "disrupting visa with a new visa."