One of the reasons, is that it would actually increase the cost of testing. This means they would pass that onto you the test taker. The reason for the increased expense is the greatly increased need for valid questions. Currently, the LSAT needs to essentially create just over 400 valid test questions a year. Since CAT tests are offered throughout the year, it is important to have an extremely large question pool to avoid the problem of having a test-taker disclose the questions they saw to another test-taker. At any given time the question pool on the GMAT, for example, is between 5,000 and 10,000 questions with some questions being changed out every month. This means that over the course of the year the GMAT goes through about 18,000 - 20,000 questions. That is a huge difference and a great expense.
Not to mention, that potential decrease to the validity of the test. That many more questions, means that much more chance of error. I teach people to take the GMAT, GRE, and the LSAT and I must say I cringe at the thought of the LSAT going to computer.