I do let DisplayCal install system-wide, but there are multiple possible reasons why someone would not want that. For example because doing so will prevent them from being able to manually select a monitor profile in digiKam, and because they might prefer to use color management systems such as Colord or Oyranos instead.
One does not “install color management”.
Nothing will be color-managed if it does not support color management. What may happen, if one sets DisplayCal to do so, is that the calibration curves will be loaded into the video card gamma table and so change the colors in the whole X system, but that is just one piece of the puzzle and does not alone constitute correct or complete color management.