“overhead cam engines like lower "W" rated oil since oil needs to flow to the cams on top of the engine quicker in a cold start.”
There is no quicker, it either pumps or it doesn’t. The same volume of oil per pump turn is moved, pushing oil down the galleys at the same rate, this morning at 52 f my Tacoma will not know the difference between a 0w20 and the 10w30 in the sump. The only way the oil will slow down is if the oil is at a temperature below its pumping viscosity.
It's "one size fits all" for engines nowadays. Bearing clearances are very precise in all new engines, and overhead cam engines like lower "W" rated oil since oil needs to flow to the cams on top of the engine quicker in a cold start. 5w-30 has been the go-to for this. Now it's more like 5w-20 and 0w-20 in normal driving conditions. I'd bump it to 5w-30 if towing or driving up mountains all the time or something. 0w-30 and 0w-40 are in more expensive overhead cam engines with turbos.
Older pushrod engines without VVT or cylinder deactivation don't care much about thick oil unless it's freezing outside. There are less parts that oil needs to flow to. Go ahead and dump 10w-30 or thicker like 15w-40 in an engine like an LS1 as long as it's in summer. They may actually sound smoother if they are very high in miles. Pushrods can still benefit from 5w-30 or 0w-30 in winter.