this will happen at any responsible web host. If you are hosting phishing sites, expect to get taken down. This trickles up. if you run a hosting company, and you get enough complaints that you don't deal with, then yeah, you will get shut down or asked to leave.
That said, I think especially for higher-priced services, a phone call would be nice. (Note: I don't call my customers, though this is a policy I've considered implementing.) I'd be interested in what other people think about other notification systems.