Errr... reading your points I presume you've never really done that (notifying a service provider).
> Why don't you contact police or the site owner instead?
Police? Seriously? My police here in germany or the italian police? What do you think will happen? Right: nothing.
Site owner? If you can tell me the site owner from an IP... I will do that.
> You risk prosecution.
By telling a service provider that they host malicious content and should do sth. about it? Now that's an interesting view.
> If it's a brazen criminal using their own host [...] No customer support required.
The customer support was the only way to contact the provider. It doesn't matter if they are housing or hosting malicious content. They are at least partly responsible, especially if someone is telling them.