"Far more" is relative, to say the least. We're talking about the amount of water that fills a shower pipe - very little - and unless you're only showering once a week it's not that big of a change.
In our house, the master bath is on the complete opposite side of the house from the water heater, and we have to run about two gallons of water before it gets hot, and if we wait more than 10 or 15 minutes between showers, the water in the pipes gets cold again, and we have to run another two gallons. In other words it isn't just the water in the shower pipe, it is the water in the full pipe between the heater and the shower.
I've just started looking into either getting a tank-less water heater in the master bathroom or a recirculating system to save water. I like that the recirculating system would help with the entire house, not just that one bathroom, but it is looking to be quite expensive and wasteful of energy, unless we can do something like have switches in the bathrooms and kitchen to manually turn on the recirculator for a few minutes before use instead of running the water for a few minutes.
Look at instant hot water heaters to colocate near the fixtures; they don’t have to be powerful enough to provide hot water for the entire fixture use, just the time between when fixture use starts and hot water arrives from the primary heat appliance.
Fossil gas tankless units are nice because they can be installed on the exterior of a home and are maintenance free, but emit CO2 and can be expensive depending on your gas costs (they’re better for seasonal dwellings imho). Ideal combination is resistive instant heaters at points of use with a heat pump water heater for the whole dwelling.
They don't have to be instant either: I've seen 120V plugin models that have a small tank. No idea what's better, but you don't need a 240V hookup in the bathroom to have a "while the pipes heat up" heat source.
In my house it's a lot. Due to the shower being in a different spot than when the house was originally built so the routing is about as inefficient as possible, there's well over 100 feet of pipe between our hot water tank and our shower.
How much time does it take? In the US almost all shower-heads and faucets will only use a maximum of 2.5 gallons per minute. For me the water will get hot in about 30 seconds. So I am using approximately 1.25 gallons of water. For me that is acceptable.
You probably wouldn't need it in a single-family dwelling, but there's a recirculation system in my 100+ unit building and it works great. Once it was turned off by accident and it took almost a minute to get hot water. Multiply that by all the neighbors and it seems like a good bargain.
Like all thing in the water-energy nexus, the right answer depends on whether you live in a water-stressed environment. In California this may be a great idea, but it is probably not useful in New York.
There is no water shortage, there is an energy shortage. You can easily desalinate as much water as you want, it costs about $0.002 per gallon, while heating a gallon of water is 10x that.
Desal is 3.8 kilowatt-hours per thousand gallons while heating water 70 F to 120 F (reasonable minimum range) is 122 kWh per thousand gallons. You're absolutely right, this is a case where it makes no sense to use energy to save water.
Probably depends on your heater setup. My parents have a flow-activated central heating system in the basement and waiting for warm water can take over a minute. In my current apartment, I have an electric heater basically next to the shower and the water is warm within a few seconds at most.
