No, it's not "further" derated. That's not how the temperature deratings work. It starts from a different point. Let's look at the Romex example. 6 gauge Romex is listed with a standard 60 degree C rating for general installation. That shows 55A capability. But to start calculating for temperature derating, you don't start from that 60 degree point and keep going down from there. It starts from the temperature rating of the individual insulation on the wires, which is for 90 degrees. That 90 degrees would start counting it down lowering it from 75A to some lesser value.
So then it's a "which is the lesser thing" race to a crossover point. If you derate from the 75A value, and it's really hot, so it ends up way down at 51A, then yes, you have to use 51A. But if it goes from 75A only down to 61A, you don't get to use 61A; you have to stick with 55A, because you can't go over that.
So in other words, it's already kind of pre-accounting for it being pretty hot overall, and it's rare that the derating calculation would push it down far enough that it gets below its already default lowered value from that 60 degree column.