The obvious answer to the idea posed in the title is so big prints can be made without enlarging. Indeed, my Nikon D800 and D810, with their 36.3 MP sensors, give me images in excess of 20" x 30" at 240 dpi. With files that size, large prints will suffer no loss of image quality.
However, when shooting portraits, there is another advantage, and it has to do with cropping. Before I retouched this image of the wonderful Crystal Gomez, I cropped it down to 17" x 28" to get this:
However, some photographs can be cropped different ways to yield different looks. Here is a 12.5" x 16.6" crop of the above image:
Moreover, here is a 12.3" x 13" crop:
Lastly, a super-tight crop gives us a fraction of the original 20" x 30" image, but still results in a 10.2" x 8.9" portrait:
How often I wish I had a high-megapixel camera available to me when I shot older portraits! This goes double when the model is now inactive, or has moved away. Big images are so much more versatile because you can crop them different ways and still maintain high quality. The only downside is that a lot of hard disk space is required to store and backup these big files.