The lower the temp difference between room air temp and the water heater set temp the lower the RATE of heat loss. Remember velocity vs acceleration in science class? It's always more efficient to set a water heater as low as possible. Using more cool water than less hot water is no difference when the heater has to heat up the cold water that entered it, but during standby is where losses are less.
That being said, Legionella bacteria thrive is lukewarm temps, so 140F or higher is better in this case. You can run out of water is the temp is low and the tank is smaller than you need, as a tank can only provide ~70% of it's volume before starting to cool off significantly, so a 40 gal water heater has only 28 gal of usable hot water.
A cooler tank temp will also reduce the rate of galvanic corrosion, prolonging the life of a glass lined steel tank.
The real answer is a Marathon electric tank (polybutylene, so never rusts, and no galvanic corrosion so no need for an anode rod), or a tankless water heater, or a stainless steel highly insulated tank. Actually, the real answer is solar hot water. It gives so much a bit of heat loss doesn't matter.
I have a Marathon tank set at 130F.