We are saving energy and wasting water!

Would insulating the pipes do any good to solve this problem?

Would booster pumps make a difference?

We are in temperate California, if that makes a difference.

There are retrofit recirculation pumps that install under a sink for example, and feed from the hot line into the cold for a closed circulation loop so no water is "used" They're typically run either on-demand (a few mins before hot water is needed), or set on a timer to run every 15 mins or so, just long enough to purge the line. A fairly large-capacity pump may be needed for a long distance run to generate enough flow-rate to activate a (gas, I assume) tankless.

This is bad plumbing design - not a bad water heater.

Tankless water heaters add about 4 seconds to the wait for hot water. It takes two seconds for them to put out heat and another two seconds for them to get hot water into the first 10 feet of pipe or so that would have been filled with hot water if it had been a tank system.

Yes, insulating your pipes will help reduce the heat loss between uses and keep the hot water in the pipes.

If your house is really large, then you should consider a circ pump (fixes the symptoms of bad plumbing design) or a separate heater.

I imagine we could build a cabinet for a tankless water heater on the outside of the house on the affected end of the house? Our basement is only under the kitchen. That is where we typically locate water heaters, but, now, that seems ineffective for the bathrooms.

Is it a fallacy that tankless systems save energy?

Electric tankless units only save about 3%.

The gas tankless save, not so much because of the lack of a tank, as much as the lower flue temps. Not having an uninsulated chimney up the center of the tank helps also.

A standard "energy saving" tank unit has a energy factor of .62 a regular, non-condensing tankless unit has an energy factor of .84 -.86

Do you have uninsulated pipes in a slab? That would be a serious problem.

My house is 2,550 sq ft. An L-shape layout. My master bath is at the far end of the long leg. Kitchen at the bend of the L, with my electric tankless being in the laundry room at the near end of the short leg. 2nd bath is at the far end of the short leg. Master bath is longest to get water, of course. I generally don't use the master bath except occasionally in summer, and I'd never formally timed it. Checked just now. It took ~8 mins to get warmed water at one of the master bath sinks, although that was at only 0.5 GPM flow rate. The washing machine is much quicker ... so yeah, it's all about the distance.

Note: My house was already built when I bought it, I didn't have any input on the design.

I have a 2400 sq ft single story house with the shower at the oposite end from the water heater and low water pressure. I get hot water in about 2-3 min. If your's takes 10 min you have other problems besides poor plumbing design.

Another thing to check: Some single handle faucets will allow cross flow between hot and cold. When you turn on the faucet in your shower, hot water pressure drops more than cold due to restrictions thru the water heater and extra corrosion in the pipes. This can cause cold water to flow into your hot water pipes thru the faucet or shower in your other bath or kitchen. This is usualy easy to check and sometimes fix. Just turn the unused faucets all the way to hot or cold. If this is not possible, close one of the shut off valves under the unused faucet.