When one's primary handling of numbers comes down to either linear (single-dimensional) lists or money, then you won't use modulo very much.

But any time you're walking over a discrete multidimensional list packed into a linear list, or walking over any discrete periodic signal (one very common example would be walking a linear array of screen pixels, walking over pcm samples in an audio waveform, literally 100% of GPU programming and 90+% of SIMD programming) you will want to be able to translate between "how far from the start am I" and "how far into the current cycle am I", and modulo handles that.

Similarly for almost anything involving time calculations (and for the same reason: because they are periodic). Modulo is literally described as "clock arithmetic" after all.

Here you can find Tempestt Bledsoe singing about it, lol https://youtu.be/fqtzqcJ6agE?t=570s

So you are absolutely correct that there do exist avenues in programming which can dodge this particular raindrop, I hope you aren't opposed to the idea that they are at least few and far between? ;)