I always thought people like Kang basically just got plastic surgery once they had sufficient influence to be able to afford it.
My other thought is that most of the components of ridges are a dominant genetic trait (kind of like how the Klingon ridges were prominent in Romulan-Klingon hybrids or B'Elonna), and that through a gradual process the virus-affected Klingons interbred with unaffected Klingons until ridges returned.
As for DIS Klingons, I have several thoughts. Since the Klingons go back to normal by SNW, it could be possible that they just decided to retcon the DIS style away all together. Another weird thought is that they could be some sort of genetic glitch encountered with augment-normal hybrid Klingons where they got the ridges but their melanin's all wonky, resulting baldness and either albinism or an "anti-albinism". Once again, the interbreeding meant that eventually, these traits disappeared.
To explain why we tend to see the same type of Klingon together, there could be social biases to keep oneself surrounded by the same type of Klingon; this maybe slows interbreeding enough that communities of several types of Klingons still existed by the 23rd century, but had largely merged back into the normal-ish Klingon by the 24th.