Yes, children should stay in school until 16, because children are too young to decide that they want the consequences of dropping out of school. Dropping out of school has serious consequences, and young people do not fully appreciate the lasting consequences before they drop out of school. Students should have every chance in life, and that means getting an education.
Even though high school students can drop out before the age of 18, I still believe finishing up school when you're a senior at 18 is much more efficient. It just makes more sense to me be finishing school, while you are a legal young adult. Not to mention, there is still much more to be learned in those last 2 years of school.