I can envisage a practical difficulty: what if an image has got 10 keywords assigned - or, 100? There would be no way for Lightroom to "guess" which particular keyword(s) you did want to know about at this moment, vs others that you didn't. And showing all keywords at the same time next to every image thumbnail would probably not be very legible.
So: when you click to highlight a given keyword (in the keywords list), images with that show a brighter border in Grid view. A visual confirmation of how widely this particular keyword is used, and on which particular images.
You can also rapidly filter images by one keyword of interest, clicking the arrow next to that in the keywords list (or else with the aid of the Filter bar / a Smart Collection / a filter preset, filter images by multiple stated keywords).
When you've highlighted a whole group of images, the Keywording panel "summarises" their keywords. Any keyword that does not appear belongs to none of them; any keyword with an asterisk belongs to only some of them; any keyword without an asterisk belongs to all of them. Editing out this asterisk within the keywording panel, will cause that keyword to be applied onto all (instead of some) of the currently highlighted images; and deleting a keyword altogether within the keywording panel (or re-editing its text) does the same thing onto all the currently highlighted images.