Hey, Art...
Back when I cleaned, I did mainly apartments... empty ones more than 90% of the time.
I made it a point to develop the most efficient wand stroke pattern for each unit type, on each property I did. In other words, I started in a specific place, ended in a specific place and got between the two points in a specific route, for each floor plan.
My main approach went like this:
I used 230 ATW, through a #6 jet equivalency (2 x 03), at 800 PSI. (I used live solution reels and knew that I lost 250 PSI through them, so I turned up the pressure to compensate.)
When I cleaned an area, I took the mindset that I was "looking for areas that didn't come clean on the first try". When I found such areas (usually just spots, actually), I'd go over them again with a slower stroke, pulling the wand at about 1 ft. per 3 seconds or so, to increase the flushing ability, which worked about 7 out of 10 times. When it didn't work, I spotted the area again, kicked it in, and repeated. (I did carpet repair as part of my offering and knew the vast, vast majority of the time what would and wouldn't come out. And I patched or heat transferred before cleaning anything.)
The areas that I cleaned, I used an overlap of 1/2 of the wand width, so everything got cleaned twice as a matter of course. When I came to a traffic area that was ground in, I would "end" a pass (a row of wand strokes) on the side of the area closest to me, so that it was cleaned by that pass. Then I would begin the next pass at the side of the area farthest from me. This way, the area got cleaned 4 times.
I literally timed myself (glanced frequently at my watch...) on each unit, to be sure that I didn't slack off. (I had a minimum acceptable rate for myself of $75 per hour, with a target of $90 or more... $1.50 a minute, while in a unit.) And using that system, I could be in and out of a normally- soiled 1 bedroom efficiency (LR, BR and BR closet to do...) in 8 minutes. (1 BR w/ hall in 12 min.... steps took 5 minutes (I used an upholstery tool)... 2 BR took about 15 minutes)
I can see in that situation that I would have gotten about 10% fewer necessary strokes with a 14" wand. (2" = 1/6 of 12", or 16.6%, but my overlap pattern would have negated part of the 17%).
But in a production situation like that (I did up to 14 apartments in a day, with 10 being more typical), I would have preferred a wand that was more maneuverable so I could "fly" with it.
But that's just me... in that environment.
Coasting along (by comparison) in a residential setting, getting 10% more production but only doing 4 to 6 a day, max, I can't say for sure. I didn't like doing residential, other than carpet repair, so I don't have a real basis for comparison from personal experience.