Only God knows why He did not mention America in the Bible. Still, we must ask, "Why should America be mentioned in the Bible?" There have been many nations throughout history that have risen and fallen that were not mentioned in the Scriptures either. So, it could always be the case that somebody in some nation would ask why their country was not recognized in the Bible.
The Bible makes no mention of the United States, Mexico, Canada, or South America. Nor does it speak of Australia, Madagascar, the Antarctic, the Arctic, Greenland, Iceland, Japan, Korea, etc. There are far more countries the Bible has not mentioned than those it has.
At the risk of sounding a little judgmental, we must be careful not to think too highly of ourselves, particularly regarding the greatness of the United States and somehow think that we should be mentioned in the Scriptures.