> It could be as simple as just forcing companies to source responsibly and only work with suppliers that have some really strict policies against using child labor.
They are already doing that.
The problem you have is that it is impossible to figure out where an atom came from.
The waste majority of cobalt is mined in traditional large operations. Only a small part of cobalt comes from small mines and only a small part of that is done with child labor.
The major cobalt buyers already work only with the big traditional mining companies. However there is a simply demand for cobalt and somebody will the smaller artistically mined stuff. There are many buyers who don't care.
Cutting out the whole mining sector outside of the large producers would also not be very ethical. There are programs underway to validate and certify some of these smaller mines but there are far to many to seriously do that from the outside.