There is one glaring problem with your proposal. There isn't a shred of any evidence to support it.
It's the sort of idea which was popular 150 years ago or so, but that's because 150 years ago archaeology was in its infancy and genetics didn't exist. In the absence of much in the way of useful evidence, there wasn't much solution except to make things up off the top of your head. Especially in the absence of genetic evidence, the most obvious ways to divide people up was based on their most obvious external features - things like skin colour.
Thing is, the origin of different skin colours doesn't require thousands of years of seperation. As pointed out upthread by Coyote, the distribution of skin colour shades correlates remarkably well with latitude - higher latitude populations have lighter skin. The most common explanation one is the simple one - more melanin (and hence darker skin) protects against the harmful effects of UV; but it also hampers UV's benefical effects - UV catalyses vitamin D-12 synthesis. This means that the further you get away from the equator (and hence a lot of sun), the less dark skin has to be to protect you from harmful doses of UV, but the lighter it has to be to allow enough UV for effective vitamin D synthesis.
Ignoring very recent population movements, there are a few populations that buck this trend - black people in southern Africa, for example, and light-skinned people in tropical south-east Asia. As it happens, though, both these cases match well with archaeologically and linguistically evidenced recent population expansions (with 'recent' meaning in the last few thousand years) - the spread of Bantu farmers from equatorial Africa southwards, and the spread of Austronesian farmers from China. There are a few other odd cases - Tasmanian aboriginals were darker than you would expect, for example - but on the whole the picture holds up.
This skin colour distribution doesn't require isolation to evolve, either. The distribution was maintained by natural selection - peoples with light skin colour would be at a selective disadvantage at the equator, so the alleles for light skin would be selected out over the years in equatorial populations, no matter how much people interbred with neighbouring populations.
And people did (and do) interbreed with neighbouring populations. The level of genetic diversity in modern humans is surprisingly low for such a widely-distributed species. This is the most commonly presented piece of evidence for the idea that the modern human population is the result of a rapid population expansion from somewhere in Africa within the last 70,000 years, with only limited genetic contribution from populations elsewhere.
If what I am saying is not true then how come so many Arabic peoples and many Chinese type peoples have light skin even when they come from very sunny climates? It clearly is because light skin is dominant over dark skin. They are mixed race.
The Great Wall of China:
Light skin is common in China because China is quite far north. Modern China extends from about 20° to about 55° North - equivalent to northern Africa to southern Scandinavia; or from Mexico to Alaska. Now it is true that light skin extends farther south than would be expected if we just looked at latitude, but that was one of the two big exceptions to the pattern I mentioned. The problem goes away if we accept the standard hypothesis that famers spread rapidly from China throughout southeast Asia and the Pacific in the recent past, as archaeology seems to demonstrate.
Why would a people who evolved in the baking deserts of Asia have evolved light skin. The answer is they didn't evolve there. They are a mix of the original Scandinavian race and the original Indian race!
You are correct that Arabic populations seem to have lighter skin colours than you'd predict from UV (look at page 18 of this article if you want some numbers - this is calculated based on actual UV exposure rather than simply latitude). This could well be the result of recent population movements, but the problem with your model (northern Europeans moving into West Asia) is the same as I pointed out before - there's no evidence for it. On the contrary, we have evidence for people moving the other way - agriculturalists from the Middle East colonised Europe in the last 10,000 years. The Middle East has been at the crossroads of various conquering empires in historical times, as well as the centre of trading routes linking Africa, Europe and Asia, so the population movements caused by this could be something to do with it. That's just my speculation though.