The real thing is calibrated in a way that your inkjet can't be, and the inks/pigments in the ColorChecker are chosen for good metameric properties (look it up, you'll learn something) and resistance to fading and changing over time. I've had mine for about 30 years, and it's still in good useful shape. (It will deteriorate if you leave it out under bright light and sun for long periods of time.)
The patches are also chosen to approximate common real world colors, darker skin, lighter skin, blue sky, etc, and to show some colors that are particularly difficult to reproduce.
I also happen to use Picture Window Pro when editing scans. It has a function that allows you to lay a grid over a scan of a Color Checker and then automates a color correction curve. You can save that curve and apply it to any photo shot with the same film under the same lighting conditions as the photo of the Color Checker.
The Color Checker is a great tool, and an industry standard for decades. Mine has cost me about US$1 a year so far.