My opinion is that it is a good idea. The road is not really needed as it is just as easy to drive to the Beckhampton Roundabout to gain access to the A4, I don't see that it will make much difference to the volume of traffic. I believe the plan is to turn it into a footpath/cyclepath in order to link up the landscape between the Avenue and the Sanctuary. There are some standing stones that are outside the Avenue fence which many visitors don't actually get to see as they are each side of the road.
The speed at which traffic goes along the Sanctuary-Silbury section of the A4 is another matter.