I don’t think a lot of people who buy unfair phones would be willing to pay more to compensate.
There are however already some organizations rating the fairness of phones or phone companies. You can find a list at the bottom of this guide.
As you say, it’s hard to define what is fair, so these rankings are sometimes quite contradictory.
Generally FP’s whole plan is to inspire other companies to become fairer and to help them FP is trying to be very transparent with their supply chain, so others can copy them.
A label should definitely be independent however, so Fairphone shouldn’t do this themselves.