I would agree up to a point but what you are describing is more a lack of general proficiency than the idea that you can't successfully switch from one manual of arms to another when the chips are down. I have been carrying and using S&W double action revolvers and 1911 pattern pistols for the better part of the last forty years as well as bolt and lever action rifles and various shotguns both in the field after game and as personal defense weapons. You may outdraw me and you may outshoot me but it isn't because I lack the proficiency to operate the weapon or the presence of mind to know the business at hand.
I think it is pretty obvious and it is fairly simple. While it is true that none of us may operate in the manner we hoped for in an emergency, we are all the culmination of or experiences at the moment of truth. We do our best and let the chips fall where they may.
I chose the analogy of operating a motorized vehicle on a public highway because that is one thing that nearly all of us do nearly every day that puts us in a potentially life threatening circumstance with other people who are similarly equipped. A potential accident situation can develop very, very quickly and usually without much warning. As in a personal defense scenario, situational awareness is the key and proficiency - yes, even expertise may be the difference between surviving the situation and not doing so. Experience and judgement are also things we all possess to varying degrees and will factor into the outcome as well. You may be licensed and insured for the operation of everything from a moped to a tandem trailer eighteen wheeler and you are expected to do so in a manner that does not endanger yourself or others on the public streets and highways. The fact that we, for the most part, are able to do so argues in favor of the ability to master more than one system. I am personally acquainted with two pilots who simultaneously maintain both fixed wing and rotary wing ratings.
I agree that situational stress is a complicating factor but as I said before, experience and judgement are going to play their part as well. I don't go armed and in harm's way as a profession but if I did I would be expected to be proficient with both handguns and long arms as well as my chosen back-up weapon in the course of my duties. Simplifying the process can help to a degree but I still maintain that if you are not capable of proficiency you may be in the wrong line of work. There are, in fact, people who should not carry firearms or even sharp objects on their person. I may be one of them someday but thankfully today is not that day.
For the record, the F -150, the Harley Davidson, the John Deere combine, a GMC two ton truck with a split axle, two different farm tractors, various and sundry implements from plows and cultivators to planters and mowing equipment, were all things I was simultaneously proficient at operating. Later I added a Triumph motorcycle, a backhoe and end loader, and a second pick-up truck with a three speed column shift. All were driven regularly or required to be moved on public highways between two farms in the area. I am not bragging - simply pointing out that although the controls were different the operating principles remained the same. Shiny side up - keep it between the ditches - don't run into things.
I can't say what works or doesn't work for you, only how I approach the situation.
It is not the diversity of machinery, but the similarity that I see as a disadvantage. No one will confuse a combine with a car. Nor the collective with a yoke. But one might be disoriented under stress between two things very similar, yet different in operation. Each to their own.