Market failure calls for regulation. There is a way to prevent such behavior from being acceptable or lawful.
That anything being our image as good people.
What good person holds an economic principle or their wallet above a child's right to have a childhood, education, their health, lives and to not be unrepresented, exploited, abused or underpaid for their labor?
We, everyone of us reading this, know the reality, if not just look around and see that lady cleaning floors or that guy in the fast food joint working their asses off for a menial pay.
You could say they are a step above slavery, but hey, no problem, you and me have good jobs and money enough so we can buy anything we want to eat and a shiny gadgets every year.
Ignoring this reality about slaves in those countries and almost slaves in our land is easy, but don't forget that this is a conscious decision.
But if you look at the electronic device we're talking about here, namely iphones, it is an overpriced piece of hardware used as a display of social status which is unrelated to a market call for cheap electronics.
Apple has more than enough margin and power to be able to secure conflict-free minerals for their devices and lead by example, but they don't because there's no regulations asking for it and they'd rather get a tad more profits for a bunch of shareholders instead of caring for other humans (who happen to be in distant countries and black or brown or yellow and poor).
The more unrest there is in those mineral rich countries, the cheaper the minerals will be and the juicier the profit for shareholders.
Why does that needs to happen? Because otherwise you get Congo. Europe used to be like that, and our forefathers fought their way out of it with their own blood.
Ask yourself - why is it that you buy food and beverages in your local supermarket or restaurant, and you're not worrying it will poison you? Why is that you can safely buy an electrical appliance and connect it to your wall socket without burning the house down? It's not because free market. It's because those segments of the market have been heavily regulated, and those regulations came to counter various shenanigans companies were pulling off.
Markets do not start regulated, they get regulated - and they get regulated because they're too good at their only job - optimizing for profitability. Regulation is there to stop otherwise profitable abuses from happening.
http://money.cnn.com/2016/01/17/news/economy/oxfam-wealth
and even with regulations in place. Companies want to grow more and more every year, even despite sometimes the market being saturated. How it that only possible? Cutting costs - Congo is what makes this possible. Congo and our will for buying such products. My point is that only people can change this, by not buying. If we don't buy, only then companies will change - You need to talk their language - You need to get to their pocket - money.
With this I don't mean that the market doesn't need regulations, pretty much the opposite. I'm just saying that most of the times regulation only is not enough.
"Not buying" isn't a bad solution per se - it would work perfectly well if we could coordinate enough people to change their shopping habits. But it's close to impossible, both because coordination is a Hard Problem, and because the market doesn't offer alternatives. People would have to reduce their quality of life, and it's not something humans generally do out of ideological reasons. There's only so much things one person can care about strongly, and those things seem to be somewhat randomly distributed, ensuring you can't get enough people to strongly care about the same thing.
Regulatory bodies, like markets, follows incentives - those incentives may be different, but the mechanism is the same. One of them is the funding from big corporations you mentioned. Another one, in democracies, is popularity. I think it's easier to convince (almost) everyone to care about some issue enough to change their voting patterns than it is to make them stop buying stuff. Therefore, the regulatory change may be easier to achieve than "vote with your wallet" market change. That still requires a lot of coordinating effort though.