In a perfect world I would agree.

In practice giving a GAI sufficiently high to cover all reasonable needs would be no guarantee that they would be met.  The mentally ill, including the addicted, would not be protected by a GAI.  Neither would the poorly educated who have difficulty distinguishing between needs and wants particularly when confronted with aggressive marketing.  

If the private sector were to provide all needs their profit would inflate costs and they would be inclined to take advantage of the naive.  Education, housing and health care if provided by the private sector for low income families and individuals would also further deteriorate.