But if the 'unit of service' being provided is a full server, that may be the natural atom of enforcement... or even the only practical one.
Let's concern ourselves with the general case, setting aside the specifics of the WPMU/ServerBeach service arrangement.
A customer could be purchasing a full server, or perhaps just rack space, and the provider might not have (or reasonably want) finer-grained server access or traffic-blocking options.
Faced with a DMCA notice, and in the sort of knee-jerk cover-thyself mode of thinking that the DMCA encourages, such a service provider may have only one crude switch to throw.
Reckless/automated notifiers face few penalties for misdirected or overbroad notifications. For example, they can ignore a particular website's DMCA contact information, and just start firing away at more foundational services whose contact info can be auto-discovered, like the IP-block managers or even domain-name service providers.
Those are a problems arising from the DMCA's liability/incentive setup, not the service provider.