Casino is making profit because of that edge, if there is no edge than casino won't make profit.
Answer is in ann thread: black jack & sport bets. So, it's not 0% after all.
It's possible to have a zero house edge casino if it's a PVP casino (player versus player). All the money goes from one or another gambler, but this way the house won't make profit, so it's hard to know if someone would spend time running a service like this, making profit only from withdraws and maybe deposits. But for gamblers it would be a different concept of online gambling.
But running a site without house edge you can earn on placing ads from other gambling sites if your site becomes popular. PVP casino without any house edge would be a popular site among gamblers because many of them think that it is the house edge what beats them.