Your answer is not thoroughly researched.The genes responsible for skin/eye color come from both parents.A pale skinned male and dark skinned female (and vice versa) will produce mixed color of the skin.
The Cheddar Man-on what basis London University College got dark skin and statistically impossible blue eyes?He was yDNA
I2a S2524* and mtDNA U5b1.Their results look made up.Was the testing witnessed or was it just internal affair?He was living ~10000 years ago and the Last Glacial Maximum was ~22000 years ago so Cheddar Man and his colleagues lived in a very cold period and having dark skin could be fatal due to severe loss of body heat.Furthermore his appearance would make his hunting more difficult comparing to the pale skinned tribes...
The question is:
White people show two important markers who is present among modern light or very light skinned Europoids, one almost at 100%, the others with more moderate scores despite important among Europoids. others markers seem associated to blond hair but also to light eyes and somewhat light
er skin even if lonely we are not sure they could have the same lightening effect that the two principal ones, at the contrary we can suppose they can produce the lightest "white" skins we know. BTW most of East Asians could be put among "white people" (the less light ones), despite they don't present the same efficient marker. We don't know the exact penetrance of all these markers. We do'nt know what other markers could have a weakening imput. We dont' know what exact skin colour was the ancient people's ones, and their ancestors one. We know that at least some other markers present only among SSA people are darkening skin, so we can infere that ancient basis of our ancestors were not so dark as the darkest current people of certain places of "black" Africa. We don't even know what was the original panel of pigmentation markers, in the case we 'd know where and when decide we are in front of our "original" group of ancestors.
Plus I can't accept that a certain % of BA Europeans showed still "dark" skin in the African sense without it could have been noticed by Ancients. So what science has at hand is a progress but not all the knowledge about pigmentation markers.
Concerning overliving, I'm not sure that relatively dark skins would have been by force a big handicap: for metabolism the vitamin D could have been provided by some kind of food, and not only by sun skins absorbtion. What we have to adopt is a prudent position.
Concerning last-Paleo-/Mesolithic people,what I notice is that the European population which the most of them are the lightest ones todate for skin and eyes. Not to say that the most of their lightening process is not due to mixing with Neolithic people + selection, but they went lighter than expected; maybe due to some other SNP's inherited only from local HG's and not Neolithic farmers. Only thoughts.