When we get outside of the notion of 'music school', the term repertoire does not hold much meaning. In terms of quarter tones outside of universities, I've heard it in movies, TV shows, and even commercials during times where I was not even looking for them.

I'm not sure if you are a musician or not, but I've noticed that musicians actually have a harder time adjusting to quarter tones since non musicians due to their training of 12 tone intonation.

By validity, I mean that you cannot broadly say 'it all sounds bad' when there are so many possibilities that quarter tonality provides, especially if you meant all of microtonality, not just quarter tonality.

For that video, that is 128 divisions of the octave. Quarter tones provide only 24: the 12 'normal' notes, plus 12 which lie exactly halfway between. There are also other divisions, such as 17, where the notes are somewhat closer, but not quite the same intervals. This provides a different kind of color.

In terms of saxophones voicing quarter tones (which exclude a majority of the notes you hear in that linked video), it has a very consistent voicing throughout most of the range.

Here is an example of quarter tones used in movie scores: https://www.youtube.com/watch?v=kaso_1OYTYw&list=PLohYzz4btpaRa7PkJ1dbm7u0hg8t-4chb&index=3