You are wrong. At that time the whole universities had, if they were rich, a couple of mainframes for the whole institution, if they were poorer, one or none.
All the students wich are entitled to access to the mainframe worked typically on a single mainframe which was also used for the university accounting etc.
Mainframes were, using the more modern words, the big servers with the capital S, effectively.
Hobbyist keyboard alone (without the TV) had the price of nearly 1000 US dollars equivalent today in 1975
http://en.wikipedia.org/wiki/TV_Typewriter
The cheapest self containing computer that year had a minimal cost of 30,000 of today's US dollars.
http://en.wikipedia.org/wiki/IBM_5100
The "operating system" of it were Basic and APL, and it had the storage of 200 KB.
Now compare all this to the "server" which started this discussion. The claim was that when Gates started he didn't need "servers."