Yes, it would make sense to have children test into schools of their ability, because the current education system is broken. Right now, children are placed in the same grade based on age, even though their abilities within that grade vary widely. Education is targeted only for the average. Children who are exceptional deserve an education on their level.
Children who are going to succeed are going to succeed no matter the school. However, that is how it is as the system currently stands. If the United States made it so that you had to test into schools, then the schools where the less gifted children were sent might become more mediocre. The teachers would expect less from the students, and would, accordingly press them less hard. They would see their jobs as less important, because they would know that their students were the dropouts. It would create a bigger gap between the upper and lower classes, and would not end well. So no, children should not have to test into schools.