Your "let them go to school" is the equivalent of "let them eat cake": if they could go to school they probably wouldn't be working in a mine in the first place :/.
If you want to try to solve the problem through some random intervention you need to take a step back and fix whatever is preventing them from going to school, not arbitrarily taking away their jobs and then patting yourself on the back for a problem solved.
Taking away the job does solve the problem though, because the cobalt must come from somewhere, so the mine will increase prices to pay for the new labour they need. And the tax from this will pay for the schools.
The ultimate reason it doesn't happen is because people in the west don't want to pay more for their smartphone (they are not to blame though, as they won't see this picture, our politicians, corporations and planners are the groups that maintain this picture deliberately).
You are talking about a country with child soldiers and indentured service. Your perfect-sphere-of-a-market is even further from reality than in developed countries.
If you want to try to solve the problem through some random intervention you need to take a step back and fix whatever is preventing them from going to school, not arbitrarily taking away their jobs and then patting yourself on the back for a problem solved.