I noticed from you suggest that when you do back and biceps together you still warm up biceps. Why? Aren’t they warm enough after 7 or 8 sets of back movements, in which biceps are heavily recruited as a secondary body part? And likewise with triceps when you train them after chest?
You are correct. Biceps do get a lot of secondary work during back exercises and the same is true for triceps when training chest. However, neither gets direct overload through their muscle specific ranges of motion.
I think it is a good idea to warm-up or acclimate biceps and triceps before you perform your working sets. This allows you to introduce heavier weights within the range of motion you are about to use.
An efficient warm-up for biceps and triceps will get you ready physically and mentally for direct overload and to help guard against injury.