You can set a temperature on a thermostatic shower head and you just adjust the flow of water. Most newer bathrooms have thermostatic shower heads in Europe. But even the old ones with hot + cold valves allow you to not only set the temperature but also the flow.
This is due to the law. Flow rate through a shower is limited. There is no point having an adjustable rate if everybody wants more than a legal showerhead can provide.
I guess it's a regional thing, the single "US" faucet is something I guess no one in Slovakia or Czech Republic has seen. I remember when we were on a first US business trip and it was hilarious to find out that I was not the only one of the group who tried to find Youtube videos how to control that thing and also to switch between the shower head and the tap. The second thing was that after having a shower I wanted to switch on the bed lamp - the switch was a small knob which I tried to push but nothing worked, then I found out I had to turn it in any direction to cycle between on and off.
Those are common in U.S. hotels but virtually unheard of in homes. Most U.S. homes have separate hot & cold knobs running through a single faucet/showerhead, with a knob or switch to select shower vs. tub. First time I ran into the single-control shower, it took me a while to figure out how to work it as well, and I've lived in the U.S. my whole life. It was pre-YouTube as well, so I just had to fidget with it.
I've seen the thermostatic faucets before (I assume those're the ones where you twist to adjust temperature & pull to adjust pressure). They show up in more modern upscale hotels, and in people's homes when they've remodeled their bathroom. I think they tend to be an aftermarket add-on rather than a typical part of construction, though - no idea why, they're much more convenient than the alternatives.
Also - there is almost no cold water if I switch on the shower. That's because (at least in new houses) there is a closed circle for warm water and the heating system cycles the warm water (2 pipes of warm water + 1 pipe of cold water for each water outlet) in the pipes to keep it ready for use. You have instant warm water.
You should try Arizona in the summer next time you're in the USA - we have instant hot water 24/7 - even our cold water is hot.
Yes - I'm serious. In the summertime, our water from the "cold side" is typically luke-warmish at best. From the hot side, we can actually turn the temperature down on our water heaters and save some money.
It gets a bit better during "winter" (in quotes because right now, the temperature is around 32C - yep, shorts weather in the middle of November!).
Anyhow - you can purchase the tankless circulation system you describe, but it isn't cheap so you only usually see it on new houses, and only as an upgrade. Retrofitting old houses just isn't really possible without a complete interior teardown. The only other option is tankless water heaters, but those require a decent electrical circuit to each sink. So, most of us just have the central water heater tank, and when we want hot water, we turn it on and let it run (ain't like the water is going to disappear, thanks to the "water cycle"). Or we deal with the cold water (except here in Arizona - where again, our cold water is warm).
Electricity and gas are relatively expensive in Australia compared Europe or US, so I’m lead to believe. Might be better in a new house with good insulation on the pipes.
I think most US showers have just a single faucet where you can control the temperature but not the pressure/flow. You always have to go from cold to hot (it looks like this: https://www.americanstandard-us.com/-/media/sites/asus/image...)