My main tub has really low flow. So low that the diverter hardly stays up and the water doesn't want to transfer to the shower head.

I thought it was the valve so I replaced the main shower valve, spout, and shower head. It looks great but there is no difference.

I called the city to check my pressure. According to the guy who came out, the pressure at the water tower (which I can see from my house) is 60psi. He measured 58 at my meter. He measured about 55 or 56 at the shower head. So it doesn't seem to be a pressure issue.

The main line is a 1" copper pipe. This is reduced to a 3/4" for the middle part of the run, but all feeds off that 3/4" pipe are 1/2" lines. This is true for every faucet, appliance, the tub and shower in the master bath.

What are we missing here? Do I need to replace all the 1/2" with 3/4"?