The built in calibration of such monitors is to let them re-calibrate their built in emulation modes, where they emulate the preset color spaces (such as sRGB, AdobeRGB etc.). Such modes are useful for displaying output from systems or programs that are not color managed.
Color profiling such as that provided by ArgyllCMS/DisplayCAL is for color interchange and management via computer systems. The aim should (ideally) to run the display in its widest gamut/native mode. So you would normally select this mode as the one to use when calibrating/profiling and using the display. This could be something like a “user” setting mode.
If the display lets you have control of the white point and brightness in this mode using its built in controls (OSD), then use them. If it doesn’t, then you can fall back on using your graphics card VideoLUT hardware to do this. So the calibration step consists of the option of using your OSD to meet your target white point and brightness, and then an automated calibration process for setting the graphic card 1D VideoLUTs to set the tone curve and final white point and brightness. The last step is characterizing the display to create an ICC profile. The VideoLUT calibration curves are added to the ICC profile so that they can be automatically loaded into the graphics card when that profiles is the one being used. Color Managed applications then make use of the profiles to display color correctly on your display.
The main advantage of color management is that it lets you make full use of your display capability - you aren’t artificially restricting its gamut - and a color managed application can simultaneously display images encoded in any and all colorspaces at the same time.