shouldn't "we" learn the languages of countries we visit, work in, or invade?
I think requiring immigrants to learn English is an idea that ignores history and ignores too many Americans' cultural ignorance.
The U.S. has had many communities throughout its history where languages other than English were spoken. First, there were many Indian communities with a rich linguistic tradition. Second, there were many Spanish communities which were absorbed into the United States by various means. Finally, there were many communities founded by immigrants where they spoke their native language for a generation or more. This was especially true of German immigrants back to the Revolution and Swedish immigrants in the nineteenth century.
Americans have been tourists to many areas of the world without even knowing how to say, "Thank you." After all, "they" all speak English. Many a business deal has been lost because many of the ex-pats haven't or even refuse to learn the local language. Unless an invader has "overwhelming force", an invasion and subsequent occupation will be very difficult without a large number of the invaders knowing the local language and the local culture.
If we want immigrants to "learn English", we should do far better than treating foreign languages in school as a "frill".