I really don’t know why people over-analyze things!
Back happens to be my favorite training day.
You are correct in that the back is broken down by bodybuilders into 4 parts. Some people would also treat rear delts as part of the back musculature.
Keep in mind that vertical pulling exercises (lat pulldowns, pullovers, straight arm pulldown, chinups, and pullups) will get you far more sore than your rowing exercises, just as horizontal pressing (chest workout) will get you more sore than overhead pressing (shoulder workout).
If you are progressing from one workout to the next, regardless of soreness, than you are making gains!
I think an important thing to ask when designing a routine is…
“Do any successful bodybuilders do it like this?”
“Has this method stood the test of 60 years of bodybuilding history?”
“Does this even sound rational to me - that is to me - and not some famous PT or poster on T-mag?”
If you answer no to these questions, don’t do it!
Do any bodybuilders break up their back workout aside from traps on shoulder day? ALMOST NONE!
DO a normal back workout like everyone else. Here is my routine:
Rear delt raises
Deadlift or partial deadlift
Shrugs (done on shoulder day)
That’s 2 for width (vertical pulling), 2 for thickness (horizontal pulling), 1 for rear delts, 1 for lower back. Nearly every successful guy with a big back does it this way.