For a good back.
technically you are right as the back only pulls the elbows backwards, and the upper back pulls the elbows upwards.
there is some argument for pulling the elbows down and backwards though as the pulldown/chin does.
but there's so much overlap that rows could even be on its own as the only requirement.
same goes for all other movements...chest is elbows forward and across- so only needs flyes or bench.
biceps only bring the wrist upwards towards the shoulder..so only curls- of any type.
triceps the opposite.
and so on.