For 30 years our home ran off a 1/2" propane
line. 4 burner kitchen range w/ oven, 2 direct vent wall furnaces, and 1 regular wall furnace
. We never had any problem, but when we added an aditional direct vent wall furnace
and 2 tankless hot water heaters (to reduce the electric bills) during a remodel, we upgraded to 3/4" propane lines.
I doubt you'll ever experience any difficulty with 3/8" lines. If you were going to use a couple of turkey-sized deep fryers and cook on your range while someone was taking a shower and the refrigerator
door was standing open it is conceivable there might be a problem. Personally, I'd have the deep-fryers on a separate propane container rather than off the TT plumbing anyway.
My perspective to add to your
& Ann K.