There are many, many reasons parents choose to homeschool. The US education system may be successful in the eyes of some, and yes, certain children will thrive in that system. But good teachers and administrators can be hard come by, as well as safety issues in schools these days.
But to answer your second question of the guarantee of parents meeting the standards- you can't. Some states require more than others, some require yearly testing or less often. Some require you to submit a complete portfolio. A lot of states simply require an intent to homeschool form and an attendance record.
But most parents who choose to homeschool do so with the intent of educating their children to become well-educated and well-rounded adults. Every so often you find ones that really should NOT be homeschooling, but that is not the norm. I don't find that I need to teach to the "educational standards" so many of those standards are useless and won't be used outside of a school setting. Teach them to read, teach them to learn- and they will be able to learn anything they want to throughout their entire life.