To use your Armenian example, it could be that while being Armenian doesn't actually affect your driving, a "true" model could still end up being bad for Armenians if being Armenian is correlated with the things that actually do affect crash risk.
But what about this: we don't need to solve all social ills every single time. What if we let the algorithm correctly decide crash risk, and if we notice that it unduly impacts Armenians and that's not an outcome we want, we via a separate channel compensate the Armenians? That is, acknowledge the fact that Armenians may crash more, but give them a government subsidy to offset the higher premiums, and work to bring the premiums down (i.e.: fix the underlying issues that being Armenian is correlated with).
It's related to something I've been thinking about lately with regard to minimum wage. I like the idea that everyone should have a livable income, but tying the implementation to businesses that have low wage jobs seems like mixing concerns. For example, my company doesn't have any minimum wage jobs, but shouldn't my company chip into this social ideal same as any other?
What if we let the businesses pay whatever the market will bear, and if we decide that as a social concern people should get more than that, we subsidize them from the government, which is wear this concern is coming from in the first place.