Sure, Apple has more leverage, considering their size, but that also comes with its own set of problems. Plus, their customers have nowhere to go to in protest - all other phones are full of conflict minerals too.
I feel sick when apple says they are deeply committed to upholding human rights, while they continue manufacturing electronics, because I need authenticity. I would like Apple to use more of their resources to figure out how to do conflict-free consumer electronics.
I would like that as well, but I understand how that's difficult for them to do, too: making public that you're working on that, is also making public the deficiencies you have in that area currently - something many consumers are not aware of, and of which they may think it applies only to you.
That's why initiatives like Fairphone's are good. That said, I've followed their blog  for a while, and occasionally they've been part of initiatives of which other phone manufacturers have been part as well (I recall something about Nokia and Congo). I think they just don't publicise that for the reasons I outlined above.