LN does not "steal" anything. Even with LN you must do some real transactions (at least two, to open and to close a payment channel). These transactions will have fees like now. It is only a way to "bundle" transactions.

And LN in my opinion does not fit all user cases. It's a better alternative for centralized online payment systems like Coinbase's wallet-to-wallet payments. With the same logic applied, these services also "steal" transaction fees from the miners.