French banks are actually doing that! SG/Société Générale, a brick and mortar bank that costs a hundred dollars a year, built Boursorama, an e-bank that's free and that gives you $200 if you subscribe. Advantage: SG has too many manned agencies and can't justify preemptively mass-firing them yet – they first need the customer base to dwindle. Better IT, usage of Internet techniques at the core, and drastically simplifying the product line is an intended consequence.

Same happens with other French banks. As a personal PoV, banks' manned agencies provide bad service (from 20x delays to plain mistakes), so I won't cry for them.