Let the OS do the color management, not the application(s).
Trouble is, that's not what happens. Windows doesn't do colour management. It provides the WCS library that programs can call to do colour management, but Windows itself does nothing except provide that library and the framework for linking colour profiles to devices. (I'm less familiar with Mac OS, but I think it's similar.)
It would be nice if Windows did colour management, but without a redesign of libraries (and hence of programs) it would be difficult. In general, Windows doesn't know the colour space of data being sent to the monitor or printer, so it can't do colour management.
AFAIK (it works here on W10) Windows has Color Management via Control Panel and profiles can be added.
All Windows does is to store a list of devices and profiles associated with each device. This means that a program writing to the monitor can ask Windows for the profile. That is all Windows does. Any colour management is done by programs, not Windows.
Are you thinking of the fact that when you calibrate and profile a monitor, the appearance changes in all programs? This is the calibration, not the profile.
Remember that calibration and profiling are two quite distinct processes, even though they're done at the same time by the software that comes with colormunki, Spyder etc (or Argyll s/w).
Calibration alters the state of the monitor by means of a Look Up Table, normally implemented in the display driver, which alters the white point and tone response curve (TRC) to some define state (e.g. D65 and gamma curve of 2.2, or whatever is chosen). Because this is implemented in the driver, it affects all programs (except games or video players, some of which bypass the driver). For most monitors, this doesn't affect the colour space.
Profiling, normally done immediately after calibration, measures the resulting white point and TRC, and measures the colour space of the monitor, and puts the resulting information in a profile, which is then set as the default profile for the monitor (in the list visible in Control Panel). Only colour-managed programs use the profile, and only colour-managed programs convert the image from image colour space to monitor colour space.
Application should then instructed to use "Let the system Manage Colors" (or something like that).
Perhaps, but this isn't what happens I'm afraid.
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Simon