Just to prove, I too can ask dumb questions.
1. Do you get more water from a bigger pipe, if the answer is yes, why.
2. Would 3/4 between the mixer and shower head not be filled enough with 2 1/2" pipes feeding the mixer?
I promise to have more questions no matter the answer.
Flow rate is a function of pressure, length and restriction (size). Smaller pipe like smaller wire has higher resistance.
Once the larger pipe is full it doesnt matter it will only flow out at the rate you put it in.
I have city water and very high pressure so in my case the difference in pipe size most likely wouldnt have mattered.