That is a good idea, though I favor chalk boards. But it would be great. In order to bring it about a lot of difficult management problems would have to be solved. For instance, people are going to be turning tricks in all those separated rooms pretty quickly.
My old university library had private rooms that you could use to get away from the crowds. They were sound proofed, but had a giant glass wall that faced towards the rest of the people. You couldn't turn tricks there unless every onlooker was in approval.