and the only difference I can see in starting with an empty tank is speed on those first few gallons. If you are absolutely desperate for a hot shower and don't mind running out in the middle of it, finishing in cold water, it might be a plan.

However, you are going to use the same amount of energy to heat 40 gallons of water, whether you do it all at once or start with a dry tank.

The best way to save money is to turn down the temperature in the summer, when you're not using the hot water for heating.

(just theoretical at this point)

Heating 10 gallons in water, and heating subsequent water, beats trying to do all 40 g at once?

(It's in the process now, so it's really a theoretical discussion).

In fact, starting a tank based heater without the tank full could damage the heater. Just start it back up.