Just came across the NYT’s recipe for cc cookies. The recipe calls for 81/2 oz, of bread flour and 81/2 oz. of cake flour. Because one would think the gluten factor in one would cancel out the other why not use a/p flour? That was not my question originally but now it’s mine.
Commercial bakeries used to keep 2 kind of flour on hand, bread flour and cake flour, so blends of the two were not unusual. I would think a 50-50 blend of bread flour and cake flour would wind up with a protein content at the low end if not a bit below that of AP flour. (13+8)/2 = 10.5
Personally, for cookies I use bleached AP flour. (That’s about the only reason to keep bleached flour on hand.)