She regularly has nights where she makes $300+ in tips. If tips did not exist, the restaurant would presumably pay her minimum wage or something close (as opposed to the "minimum wage with tip" they currently pay). There is no way this would come even close to paying her the same amount that tips do.
From what I've seen, tipping is a far more efficient way of allocating resources (direct from the client to the waitstaff) than employment (client -> restaurant -> waitstaff). Not only is it more efficient, but it encourages waitstaff to build good relations with clients, and vice versa.
Removing tipping removes a fundamentally personal element from the service economy. It hurts the workers by putting less money in their pocket and reducing their economic autonomy. And it hurts the restaurants because, I guarantee you, it will cause them to lose their best waitstaff. Why work for peanuts of a salary when you can make way more in tips?
(Also, tipping is a wonderfully efficient way to discover which customers are not worth being nice to. ;) )