Here there are to opposing variables:
time to carry out the drills Vs good team working
If you split the crew in two, you can do the drill in a shorter time, but at the expense of team working and all its safety benefits.
I advocate for the team working, more time consuming, approach. It is my opinion that the old Aviate-Navigate-Comunicate and Manage means:
1-both pilots Aviate (one handling, the other watching carefully and making sure that the handling pilots is handling and that the handling is adecuate, assissing him and bringing to his attention any discrepancy or doubt about the flight path, automation modes, etc...). PNF will not carry out anything else as long as the Aviate part hasn't been assured
2-both pilots Navigate (one handling, the other monitoring, assissting). PNF will not do anything else until the Navigate is assured
3-both pilots Communicate (one using the mike and talking, the other paying attention to what is said, then both making sure the other one knows what has been said). The communicate part has to be done, if necessary (sometimes it is not). If there is any necessary communication, it must be done before managing the drill. Otherwise the crew can go on with the drill directly
4-both pilots Manage (the PNF carriying out the checklist, then both pilots assessing the situation, then making decision)
YOu can save time but letting PF do Aviate and Navigate while PNF does comm and checklists. The question is: Is time so important?? Most of the times, it is not, in my opinion. It is better the team approach than the time approach, except when circumnstances are very critical, when time can be the top priority.
I have observed that many captains have the tendency of neglecting flight path while they monitor what the F/O is doing in the overhead panel after they have prompted them to start with the drills. I have seen this happen many times in the sim. A very clear simptom of this is the THR LK single chime every 5 secs, for instance. In such cases captains destroy the team and pull the F/O out of the Aviate-navigate, while they does neglect it as well. This is very dangerous, and there is no reason to rush (normally).
You have to be very very good to split the team and still ensure Aviate, Navigate, Communicate and monitor the PNF's Manage with the same level of redundancy that you can obtain working as a team.