You're also insultingly wrong with your geography.
Luke 17:1 Jesus said to his disciples: "Things that cause people to stumble are bound to come, but woe to anyone through whom they come."
Ideally, it is a dual solution of don't buy the unethical kind, and set up an alternate ethical supply chain to the same region so workers can switch to a better work place.
But, if the latter is not possible, one can at least help decrease the market for unethical cobalt by ceasing purchase.
Plus, it is not a matter of seeming morally superior. If one option is morally better than another, it should be chosen, regardless of the consequences.
So, for instance, if Jesus is correct, that it is immoral to be a path of scandal, then one should choose to not be a path of scandal, even if the state of the world otherwise remains unchanged (e.g. unethical cobalt mining continues).
In the case of rubber the big companies do provide better jobs for the families they employ than anything else, ensure the family gets modern medical care (as opposed to "witch doctor" care anyone not working for them gets), and the children do go to school and so have the ability to get a better job latter. The companies looks the other way in harvest season then families are taking their kids with them to work, so long as the kids are in school. Child labor for sure, but you can honestly argue that the children are better off despite that.
You can decide if you accept that as better or not, but it is a reasonable argument that child labor isn't always the worst possible.
Sadly I don't think in the case of cobalt the above applies.
The idea is that demand for documented cobalt will go up, prices for it will also go up, poorly-documented cobalt producers will have lower demand for their product and their profits will be harmed, the ones capable of fixing their shit so they can sell more-expensive documented cobalt will do so, relieving documented-cobalt supply, and when the dust settles cobalt will be a little more expensive but most of it will be documented.
This is basic policy-building how-to-make-the-world-less-shit using market forces for (old-school) conservatives stuff, and is the backbone of one of the most important & influential strains of political and economic thinking around. It's not remotely radical or unrealistic.
So because we can't fix their situation for them, we're allowed to actively make it worse? This is such a nonsense point of view. Exploitative industry is not like regular industry. This is not a rising tide that lifts all boats, this is enriching one or two psychopathic monsters at the expense of their entire region, and possibly financing even more in other regions.
The West does not need to go in and "fix" every developing nation, but at the same time, saying "well if we didn't sell them scrapheap ships or buy the minerals their children mine, they'd starve" is a complete abdication of responsibility for the role the demand for those minerals plays in their situation. They mine them because they can sell them, that's the whole point. If you remove the entities buying them, then there's no reason to mine them.
Until you can do that, offering 'stop buying' as a solution is a waste of time.
"Realistic" is determined entirely by the values of the overarching system. The fate of the people at the long tail of the supply lines isn't valued. That's the single, solitary reason that this shit is still happening. Change that, and the system will adapt. The mines will get better, or they will be replaced with other mines that do it properly.
Stop settling for what your corporate overlords tell you is doable. We can do anything as a species if we choose to, good or bad. Our history shows it. Industry has every reason to tell you it's impossible because they don't want to spend the money to insure supply lines are ethically handled.
If we can mine coal in the United States without children and with relative safety, they can mine Cobalt in the same damn way. Cobalt doesn't by virtue of being cobalt need to be pried from the Earth by children.
oh you didn't know? The blood of the children is what christens the cobalt such that it works in computers...
/sarcasm
