Imo Adobe does not do it always "right" - and making a dedicated profile may well improve the color rendering. This is of course already done by Adobe (and any other RAW converter that works on a cameraspecific basis), but it is not done always right and maybe the software developer may also have tuned the outcome to what he thinks to be most pleasant. You thus improve the color rendering of the camera - which may be somewhat off for various reasons: the camera manufacturer has purposely chosen to or there may be a variation between different samples of the same cameratype.
this is done for every color patch on the testchart and the results are combined so that also colors "in between" can be corrected. When now the camera records a certain patch as 59%R33%G26%B, whereas the original color patch was made with 50%R37%G24%B, the profiling software will generate a correction factor so that the patch on your (calibrated) monitor shows up as the color it should have. When you take the testshot of the testchart, you essentially have a image with a lot of different color patches - and the RGB values of each patch is more or less exactly known. Profiling thus makes it possible to improve the translation that Lr makes based on the information the camera generated file recorded. then you shoot a image of the supplied testchart, show it on your monitor, adjust the white balance based on the supplied patch in the testchart and then the appropriate software makes a camera/lens specific profile and stores it in a place where Lr or Ps can find it after shutting down and started up again. to start with you need a already calibrated monitor. The Xrite profile making software does a different thing. you then can use the monitor to visually fine tune the image to your liking.
To calibrate a monitor means you want the monitor to render color, luminosity and contrast as closely as possible as what will appear when you print. I think you are comparing two quite different items.