The ledger of every transaction has only ever been a means to an end, that end being a cryptocurrency... and it's still necessary in Lightning Network as a way to resolve fraud and as a monetary backing, it's just not used in every single transaction.

In practice, a ledger of every transaction that is copied to the hard drives of a sufficient amount of bitcoin users is a terrible idea. It doesn't scale, at all. We need better solutions. Lightning Network is one that's potentially viable in the short term - and we're seeing more people play with radically different cryptocurrency designs (e.g. Iota) in the long term.