Khan Academy is a non-profit.
So what? You haven't contradicted any of my propositions.
There are many non-profit Educational organizations.
Just because they are non-profit does not mean that every activity they conduct or pursue is ultimately beneficial to the public.
The people who operate and govern a non-profit still get paid, And many non-profit educational organizations sell products or services; e.g. Just about every private and public college.
Non-profits also don't want competition, at least not direct competition within their specific niche. They still need revenue and recognition to fund their enterprise.
Also, schools do compete with one another for students and for donations.
At an organizational level; there are many schools whose administrations would favor kick out / make themselves the only university in a region, if they could get away with it / legally succeed at doing so.
I would encourage you to drop the "Non-Profit = Always good", "Profit = Evil" ideas.