I find it irritating that so many shooters believe that the law says you can only shoot a restricted firearm only at an approved range. I believe many RPAL instructors teach this, so it is understandable, but it is not true. Nothing in the federal Firearms Act says this. People are confusing the conditions of their ATT, which does clearly state that you can only transport your restricted firearm to an approved range, with the idea that it can only be fired at an approved range. The distinction is subtle, but very significant, especially when you are talking about a firing range at your home, making the ATT irrelevant (you aren't transporting the gun).
All of the other arguments apply and have to be considered, as well as common sense safety, but you won't find a clause in the FFA that says you must shoot a restricted or prohibited firearm only at an approved range.