Modern tank water heaters are so well insulated that there's very little water heat loss or living space heat gain from them. There are advantages of tankless water heaters: unlimited hot water, more closet space, can be closer to the point where hot water is used.

We're having a new house built. The cost of the house warrants having tankless water heaters. There's still the problem of the water in the pipes between the water heaters and the use point getting cold. My plan it to have those pipes insulated and on a circuit with an electric water pump. Each use point (bathrooms, kitchen, laundry room) will have a button. When pushed, it will run the electric water pump just long enough to exchange the water in the pipes with hot water. A user of hot water would push the button a few seconds before actually using the hot water.