Are there any whole house on-demand electric water heaters capable of supplying sufficient hot water for a 3 bath house or is point of use or a combination of the two a better alternative?
Tankless water heaters powered by electric do exist but they are really inefficient and require exceptionally large circuits to operate. Some pull as much as 150 amps, which is practically the total size of the average house electrical system. If you have a choice, you are always better off going with a gas-fired tankless water heater.
If you do need to stick with an electric water heater, I suggest adding a 240 volt timer so that the water is heated only when needed, such as early in the morning or in the evening. In the other times, the unit can be left off. Installing more than one water heater (in effect “zoning” the domestic hot water supply) can also be cost effective as it shortens the distance the water needs to travel from the faucet to the tap, meaning you will be wasting far less water waiting for it to get warm.