They are out there, I have one made by Grohe; I'm sure other companies make them as well. The particular one I have is a temperature-controlled valve (as opposed to a pressure balance valve). It may also have some pressure balance functions in it. One or the other is required in replacement/new construction to help prevent scalding hazards if something like someone flushing a toilet or other water use changes the amount of hot verses cold water available.
On the one I have, there are two knobs - one allows you to set the desired temperature (it then adjusts the user set flow to make the output the set temperature) and the other sets the flow.
This is not absolute, but the temp controlled valves probably all do what you want, while only some of the pressure balance ones do. My unprofessional opinion.