I would say that 'statistically' a Captain would do the flying when an approach was considered more demanding, i.e. a non-precision one, why stick your neck out and give it to a F/O whose skills one might not have had personal experience of, so if 'statistically' more Captains fly NPA's then 'statistically' most of the NPA accidents would happen when a Captain was flying.
One assumes that both crew members have been adequately trained in their respective roles. Notwithstanding that on a monitored approach the FO is the pilot flying the autopilot would normally be utilised.
The monitored approach concept frees up the Captain from the task of flying the aircraft with, I would suggest, a reduction in the workload. Also if on reaching minima there is no visual reference the FO will stay on instruments and execute a Go Around.
I agree that there is more than one way of operating an a/c but speaking personally I have found it a very effective and I would suggest safer way of operating the a/c in conditions of lower cloudbase and/or viz. Of course I take your point that anything can be proved with statistics and am aware of the Disraeli quote.