Er, tights are worn in America! But called hose or pantyhose, IRRC.
Yes the sheer ones are called pantyhose in the US. I cannot speak for every American woman, but I have not worn them since about 1995. I live in Florida, but I have not seen them on anyone anywhere else in the country in a very long time. I do think that they may still be worn in places like New York City in more conservative professions.
In the US, "tights" usually mean opaque hosiery. You might see those in colder climes in the winter, but nowhere else.
You will probably remember that in Meghan and Harry's engagement appearance, she was not wearing pantyhose/tights and was roundly criticized for it, including on MN.