Well there is one advantage..............
Lowering engine temp lowers intake manifold temp and engine compartment temp.
While it isn't much it isn't nothing either.
Lower intake temp means lower air temp which means denser air which means more fuel is added on each power stroke.
This is why MPG goes down.
This is also why "cold air intake" sellers recommend lower temp t-stats, it makes their product look like it did something, lol, when it's actually just the t-stat.
Cooler air is also why people notice they "have more power" in the winter, cooler outside air, and why MPG is less in the winter.
Is the lower temp good for the engine, no, best lubrication happens when engine coolant temp is 200-230degF, all oil weight/viscosity is measured at 212degF
Is it good for MPG, no, see above
Is it good for power, yes, the more gas you can burn the more power you get.
Would you notice this power difference?
maybe, it would depend on outside air temp, and the air temp system on the engine, older systems had separate air temp on the intake, newer have MAF sensors on the air filter.
All fuel injected systems have ECT sensors, these are the EFI system's "choke", it tells computer the coolant temp so computer can set fuel/air rich when engine is cold, then lean it out as engine warms up, if it doesn't warm up then it stays a little rich, you also often get a CEL because it isn't warming up, computer has a timer for engine warm up, 10 minutes I think.
Would it win you a race, no.