I'm temporarily in a rental that is a large one-story house with an ancient gas fired water heater. The pilot light is very large and it alone uses about $8/month. In addition the heater is about 30' from the main bathroom.
A plumber came by one day and I asked him whether an electronic ignition could be fitted to the heater to eliminate the pilot light. He said no.
I am now considering installing a tankless electric heater in the bathroom under the sink.
Experiences appreciated.