Growing up in the USA my father told me that carp weren't an edible fish. As I grew older I learned that it is widely eaten in Asia and even Europe. Why aren't they considered an edible, albeit invasive species?
Its a matter of species, availability and culture.
We have invasive European (and now Asian Grass) Carp in the USA. The European species are muddy and unpalatable to our palates because the USA has been a wealthy nation with rich natural resources for some time. Most people haven't had to stoop to eating "trash fish," (blue crabs used to be free bar snacks along the Chesapeake) so it never entered our culinary repertoire. There has always been an abundance of much more tasty fish to be had cheaply; cod, salmon, what have you. Whereas many parts of Europe and Asia were dirt-poor and overharvested for centuries. You didn't waste what you could eat, even if its bony and gross. Carp is the Pork of fish; it turns anything organic into edible protein and can live in filthy, low maintenance environments. So Europeans with a history of eating European Carp would continue to do so as a cultural connection (or maybe they cook it better).
Asian Grass Carp are actually rather tasty. I had it for the first time in China and having also had European Carp, I was amazed by how good it was. They're not as cosmopolitain in diet as European Carp. They're mostly planktonivores/herbivores which means they need clear water, but people in the USA associate them with the European Carp we all know to be trash and ignore them when they should be eating them. But as they're mostly vegan, they're not that easy to catch. Unless they happen to jump in your boat.
There are a lot of different species of carp in different parts of the country. Where I em in the NorthWest there are better eating fish than carp around, so they're not considered desirable.