Your second paragraph is not, in my understanding, the goal of a hidden service: that is merely the goal of Tor itself and would apply to a non-hidden service being accessed via Tor. The goal of the hidden services feature is to allow hosts to have the same level of anonymity as users, making it nearly impossible to shut them down or know where to tap their traffic (for timing attacks).
Onion services can have various goals. Hiding the server is a very common one, but it's not always the case.
For example facebook runs an onion server for their service, they don't need to hide the service itself. So they configure their Tor relays with no anonymity on the service side (HiddenServiceSingleHopMode 1) and get better performance.
Such non-anonymous onion services can have many goals, for example:
* Reducing load on Tor exit nodes
* Providing users a secure, authenticated connection without depending on the CA system (assuming you got the URL through a secure channel the first time, you know only the key holder can provide service on that host).
* NAT traversal for services that otherwise have no need for anonymity
