> Of course, the water starts out cold (because the water in the hot water pipes are cold)

No, this should be considered a failure condition for a constant temperature shower. I don't care how they do it, just bleed the cold water into a separate pipe off to the side or something.

We have sent people into space, I want actual uniform temperature water.

ah, you want this, which also exists: https://www.finehomebuilding.com/2013/03/07/hot-water-circul...

the way I do it is just turn the shower on about 30 seconds before I get in, which works the same with half the piping and less energy loss due to circulating hot water (but some water loss)

I've seen a few apartments in Asia have small electric water heaters right before the faucet. They provide instant hot water until the main boiler's hot water arrives.

This is fairly common in newish kitchens in the Netherlands too, especially if the kitchen is far away from the boiler. Sometimes even with a boiling water tap, so you don't even need a kettle anymore.

A toilet flush should either:

- not drop the pressure of the cold water at all

- drop both the hot and the cold equally (due to house input being limited)

The hot water is fed by the same input pressure as the cold, so they are the same pressure system. A temperature drop on a toilet flush is a pretty big fuckup by the plumber in the bathroom.