I think there is an opposing argument to the benefits you claim could be achieved. By having free income, there is less of an incentive to work, there is actually a large chance productivity would drop, not increase!
Also, keep in mind you need funds to run the tax collection system to collect taxes to fund the basic income scheme. On a theoretical basis you may have a point but I don't see its that easy or possible in reality. I for one would just use the basic income to live and roam the world without giving anything back (since this is what I'm incentivised to do).