> If you need them to "look good", well that's art, not science.
I'm not so much interested in "look good" but in "look pleasing or harmonious together" and I think that's a question science might have an answer to.
It's no coincidence that the palette generators borrow musical jargon.
In music the definitions of minor second and perfect octave are completely uncontroversial. That these two intervals have different musical qualities, we call them dissonance and consonance, is uncontroversial too.
Sure, some cultures use dissonant intervals heavily in their music but they still recognize the different qualities. Most importantly there has been a ton of research in this field.
Contrast this with the state of the art in color science:
When it comes to color harmony there is not even a single universal definition of opposite or complementary. Look at the Wikipedia article about that topic [1]. It mixes up three completely separate topics:
1. Colors that when mixed together give a neutral hue
2. Colors that are opposite of each other on some wheel
3. Colors that supposedly have a certain effect, like contrast or harmony, when perceived next to each other
Color wheels are a dime a dozen. There is no shortage of claims that this and that color go well together but there doesn't seem to be any serious research.
I wonder if that is just my impression because it's not my field, or if maybe color science really is just not developed enough to tackle these kind of questions.
[1] https://en.wikipedia.org/wiki/Complementary_colors