There is no reliable evidence that schools improve learning outcomes either. Maybe it's all just some kids being born with higher intelligence and curiosity. If they attend a school, the school takes the credit for their achievements. If they use Khan Academy (or whatever other website) instead, the website takes the credit.
There's decades of evidence, just compare school results (even the lowest quartile) to homeschooling. I'm sure there's tons of literature in that field.
Despite our repeated attempts to do so, teaching a full k-12 curriculum is in fact not something then vast majority of parents are ready to do. Even this tool isn't vying to replace teachers. If anything it wants to replace the teaching aides (aka tomorrow's teachers who are learning how to manage a classroom). It may be worse in that regard since its eyes are on the future without considering the human element of the future.