Do not confuse captain with Pilot In Command (PIC). The PIC is the one who, as I wrote, is the "sole manipulator of the controls". The PIC changes throughout the flight...
You are wrong about this. The Pilot in Command is the captain, it does not change throughout the flight. The pilot flying changes obviously, but the captain is the PIC, the first officer is the SIC (second in command). The captain is ultimately responsible for the safe conduct of the flight, that's why he'll be held responsible by the NTSB and FAA also. I'm a captain at a major airline so I'm familiar with the rules.
There is a multitude of different reasons as to why the captain isn't always the pilot in command of the aircraft. To list just a few, these include:
-To prevent or alleviate fatigue, as it is best if both pilots take turns being the pilot flying.
-Piloting the plane is not necessarily the best use of the captain's experience.
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Allowing the first officer to be the pilot flying helps them gain confidence and experience.-In the case of a system malfunction, it may be better if the captain is not the pilot flying, as they can then concentrate on what actions to take.
https://simpleflying.com/captain-first-officer-difference/
The airline needed her to get PIC hours, not him.