Maybe the reason we haven't shot down North Korea's test missiles is that we can't. While we all certainly hope that our military would be able to successfully defend the country against incoming missiles, we need to be prepared for any possibility.
According to an article by Joe Cirincione of Defense One, the reason we don't shoot down North Korea's missiles when they fire them over Japan is because…
We don't have the capability.
Joe Cirincione is the president of Ploughshares Fund and the author of several books about nuclear weapons, including Nuclear Nightmares: Securing the World Before It Is Too Late.
According to Cirincione, when Japanese Chief Cabinet Secretary Yoshihide Suga said, "We didn't intercept it because no damage to Japanese territory was expected," this was only partially true. It wasn't a threat, but they didn't have the capability to shoot it down due to the altitude.
Neither Japan nor the United States could have intercepted the missile. None of the theater ballistic missile defense weapons in existence can reach that high. It is hundreds of kilometers too high for the Aegis interceptors deployed on Navy ships off Japan. Even higher for the THAAD systems in South Korea and Guam. Way too high for the Patriot systems in Japan, which engage largely within the atmosphere.