the Captain had been the PM during the approach, planning to take control for landing, and the First Officer PF for the approach and go-around, so it is still very much "the Captain's leg".
I wonder how many years ago, airline policy changed from the captain saying "you can do this take off - or you can do the landing?" Not "it is "your sector" or "your leg".
Over the years it has evolved into the captain's "leg" or the first officer's "leg" with the perceived dumbing down of the captain's authority to being the PNF. Recently I heard of the case where it was the first officer's "leg" on a five hour sector and radar showed storms ahead. The captain called ATC and asked for deviation 20 miles from track due weather. ATC approved the deviation. The F/O then turned to the captain, who was keeping a close eye on the radar, and said "I understood it was MY leg and that means MY decisions." The captains response was rightly unprintable.
Too many captains are reluctant to step in simply because it is the first officer's "leg" and the captain feels it is maybe wimpish to exert his legal authority to run the show. There is nothing wrong with the captain saying to his first officer "would you like to do this take off and departure?: And then when it suited him, just take over control for the rest of the flight. Where he need several breaks he simply hands over control to the first officer until it suits him to take over again. He may then use his discretion to offer the first officer the approach and landing. It is not the God Almighty "right" of the first officer to be given a leg at all - and never has been. He is employed as the support pilot in a two man crew - not a pseudo captain.