The water you use still has to be heated. The amount of energy required to heat a gallon of water to certain a temperature does not change just because its being heated at a faster rate.
The tankless water heater only eliminates standby losses of water sitting in the storage tank awaiting use. Since the element only comes on approximately 5 minutes out of every hour to maintain that water temperature, the tankless water heater is only about 10 to 20 percent less expensive to operate than a conventional electric water heater.
And tankless water heaters come with drawbacks, (According to the U.S. Department of Energy) “Sometimes….even the largest, gas fired model cannot supply enough hot water for simultaneous….multiple uses….taking a shower and running the dishwater at the same time can stretch a (tankless) water heater to its limit”. Filling up a soaking tub is another example.
Solar water heaters can provide all the benefits of tankless water heaters, but eliminate up to 85% of your water heating costs compared to a maximum of 20% with tankless.