According to international law, it is the responsibility of the US government to investigate and prosecute US war crimes and those responsible for them. As the president of the US, Obama is one of those who is responsible for this. That makes it a part of his job description.

If we don't adhere to our obligations under international law, we are putting ourselves above the law, and that renders the law irrelevant. That outcome is the one with the most disastrous consequences for both the US as well as the rest of the world.