One interesting application of taking the value appearing in majority, or more generally taking the median, is to remove noise or people from a sequence of several photos taken from the same point of view. This idea is to superimpose all the photos, and for each pixel, you simply keep the median [1].
This will have the effect of smoothing the image even if you didn't want to do that, which is part of the reason people are convinced phone cameras "overprocess" images or try to beautify you even when they aren't.
You have to counteract this by actually putting the noise back when you're done.
[1]: https://patdavid.net/2013/05/noise-removal-in-photos-with-me...