Iam installing a new shower, I have 3/4" pipe thru to the temp control valve, which is 3/4" in 3/4" out to 3 on/off 3/4 " valves, 1 for rain head, 1 for hand held, and 1 for 3 body sprays. Question should I run 3/4" pipe to each ? as they are 1/2" fittings.
My thought was to run the 3/4" to only the point where the 'balance ring' for the body sprays attaches and 1/2" the rest.

I would run 3/4 " pipe to everything but until it leaves the control valve use only 1/2"... come out of the control valve with 3/4" and reduce it to 1/2"

BTW, that copper stuff you call pipe is "rigid copper tubing"