Hi,
There is no such "written" set of rules about company flight deck management. It is left to the Captain's choice (but it will follow company "traditions"). On the ohter hand, a LHS qualified pilot is required during two specific phases: from take-off to top of the climb and from top of descent to landing.
I'm sure we will write more about all this in few (long) years when the things will be in the justice court ......
BTW .. licences are not tradition matter .. they are things required by the laws for perfom some things in aviation or any other occupations where special qualifications are required
Of course you can put a monkey on the commands of a plane or a bus .. if the travel have a happy end .. nobody will complain .. but if it's not the case .............