Central Computer Plus Stations

As in TV program episodes of Star Trek, would it not be better to concentrate power and resources into one central computer and have convenient access stations for users? This can be done on the level of one family or on the level of a community or even a town or city. Common computers could eliminate noise, heat, bulk from the user's immediate vicinity and allow them to pool their resources for a faster and more powerful computer that all can access. Are not super-computers, wireless, networks, and the Internet steps in this direction?