When I started theorycrafting after seeing the pilot, my personal favourite idea became that the Klingons we see in DSC might be the result of a genetic engineering program attempting to reverse the effects of the Augment virus that backfired as well. Maybe the DNA samples they used for reconstruction were contaminated somehow or might have not been Klingon at all, using genetic material coming from who knows what kind of sources. Members of the Great Houses would have easier access to the procedure, but many of them (like Kor) would deem it too risky or simply wouldn't want to become a 'poor man's Klingon'. In a few decades, gene therapy would eventually reach a level of sophistication that would help restore the appearance of every Klingon once and for all, noble and commoner alike.