You’re missing my point.
For domestic hot water, for the connection from whatever part of the system stays hot (the header, the recirc loop, etc) to the fixture, the amount of time and wasted water needed to get hot water to the fixture is directly proportional to the volume of the interior of the pipe, and for a fixed length of pipe, it’s inversely proportional to velocity. So you want the narrowest pipe you can get away with. 3/8” PEX has about half the interior cross-sectional area as 1/2”. This means you get hot water about twice as fast. 3/8” PEX loses about 26 psi/100 ft at 2 gpm and much less at lower flow. If you have 40 psi water and you have a short-ish pipe, that’s usually fine. Or if you have higher pressure and a longer pipe, you’re still fine.
The issue here has that, while the 3/8” PEX is near-perfect for this application, the rest of the system is not amazing. Your sink is likely (sigh) “3/8 female compression”, aka non-standard 9/16 UNEF or so, but the flow rate is well under 2 gpm, so this isn’t a big deal - use whatever adapter you like.
But your shower likely has 1/2” NPT brass female threads. To get the benefit of 3/8” PEX, you need to adapt it at the shower.
> If needed anything that required the 3/8 in, I would just use copper because it’s likely a very small and isolated case.
No, don’t do that. From the horse’s mouth (this particular horse very much wanting you to use copper):
https://copper.org/applications/plumbing/cth/design-installa...
> [Copper Pipe] Water Velocity Limitations
> To avoid excessive system noise and the possibility of erosion-corrosion, the designer should not exceed flow velocities of 8 feet per second for cold water and 5 feet per second in hot water up to approximately 140°F. In systems where water temperatures routinely exceed 140°F, lower flow velocities such as 2 to 3 feet per second should not be exceeded. In addition, where 1/2-inch and smaller tube sizes are used, to guard against localized high velocity turbulence due to possibly faulty workmanship (e.g. burrs at tube ends which were not properly reamed/deburred) or unusually numerous, abrupt changes in flow direction, lower velocities should be considered. Locally aggressive water conditions can combine with these two considerations to cause erosion-corrosion if system velocities are too high.
A 2.2 gpm shower head fed by 3/8” copper is out of spec.
I have personally seen copper tube fail when used with plain water at excessive velocity. It’s not pretty. Fortunately it was outdoors. Don’t do this inside your walls. Most vendors seem to think 8 ft/sec in PEX at 140F is fine, though.