I've had real life experience and a completely different result.
I've done some training on the 2 1/2" and it's not as bad as some make out to be, I can move it, and fairly quickly, with two people, and three make it move almost as fast as an 1 3/4", it's all in the technique.
How far do you need to reach in a single family dwelling? Again, if you have 1 1 3/4, and you add a second, how can you say it isn't going to get water on the seat of the fire any better?
As to the flow of two 1 3/4" being better than one 2 1/2", the stream of the 2 1/2" is always going to have more reach and mass than an 1 3/4". Adding another 1 3/4" isn't going to get water on the seat of the fire any better than the first and instead of using two or three personnel on one line (2 1/2"), now you're using 4 or more FF's on two lines.
I'm confused. You mentioned using 3 people on 1 2 1/2. That means you will flow (using your numbers) 325 gpm.
PDP for 200' 1 3/4"=50PSI NP+100PSI FL=150PSI and that will give me 210 GPM
PDP for 200' 2 1/2"=50PSI NP+64PSI FL=114PSI and that will give me 325 GPM
Before anyone says the pressures are too low, these were obtained by flowing my FD's hose at varying pressures to obtain the FL coefficients.