Of course, the coloring here is exaggerated for testing purposes. OSMD shows what the user specifies in the XML. In OSMD you can also set the standard colors for notes, pauses and note stems individually, or deactivate the coloring completely and leave it at the traditional black.
However, there are also useful applications for coloring in music. The fact that the notes are mostly black and white is due to technical limitations of the past. But nowaday, there is no extra price for color on digital notes.
For example, you could gray out notes that you want to be invisible or less visible by setting the color value to gray, as in some quarter pauses in the example.
The biggest application, however, is certainly in education: colored notes can make learning how to read music easier. A very special case are the patented Boomwhackers. They are colored plastic tubes that produce different pitches depending on their length. The color of the tubes and notes indicate the pitch. Of course, this can also be done with other instruments, e.g. bells. We actually have heard about this exact application case as a wish. Here is the link to the official Boomwhackers website: http://boomwhackers.com/