I grabbed some page that claimed 7 transactions per second and also did the math wrong. Not sure how that happened.

This is the big reason why I don't buy the lightning network. It won't be possible for people to have a wallet that connects to some lightning hub, since opening and closing a connection requires an on-chain transaction. So it will be impossible for anybody other than the richest few to even possess a useful wallet. Everybody else will have bits in a database they don't control.