From my experience of using public libraries (last two years or so) the main reason people go there, young people definitely, is just to use the computers and go on the internet. For that reason, I think this would be a good idea. If I'm honest, my first thought when I read this thread was that it just wouldn't be practical, but the system Rantzien outlined sounds rather good. I was also going to say it might be rather expensive, but then again I'm sure there's plenty of people (myself included) who are sitting on loads of old games they'll never play again and would happily donate to a library.
But then how do librarians decide which books to stock? Surely if they're stocking trashy romance novels and pulp paperbacks then the net is being cast pretty wide: why couldn't the same be done for computer games?