three computer one iTunes Library

iTunes is a single user application - it does not have the capability for multiple clients to simultaneously access the same physical iTunes library files. That is the way it is designed and therefore no "purpose" is being defeated, rather your expectations are incorrect.

Your primary choices are:
1. look into using the ReadyNAS iTunes Server function which will allow simultaneous access to your non-DRM music (video is not supported)
2. Use one of your PCs/Macs as a "master" which shares the media to other clients (this is the way Apple intend iTunes to be used)
3. Each PC/Mac has its own iTunes Library but the media itself is stored on your NAS (ie all clients work from a central media store, but care needs to be taken to prevent multiple PCs making changes to the media structure)
4. Search the forum for ideas on synchronising iTunes libraries - there are applications around that help do that but I have no personal experience