Someone who travels along Back Bay Drive almost daily will have better insight, but here's my opinion.
I have ridden bikes through there many weekend mornings and did not see anything that I thought was unsafe, and I would guess that is peak time for the route. In my mind, the Conservancy is overreacting.
If some form of traffic needs to be eliminated, I would suggest that it be the cars. It doesn't seem to me that the route has much value for automobile transportation. Surrounding streets would be much faster. People who don't want to walk or can't walk might say that they should be able to cruise along Back Bay Drive to enjoy the scenery. However, much of the road has a cliff on one side and the view is partly blocked by tall vegetation on the other. It seems to me that existing scenic parking spaces would offer better views.