The missing villages are more a result of limited processor/program abilities than any simple design choice. If you look at the earliest games in the series, villages were everywhere but GPU loads were exponentially less back then than now.
Daggerfall had roughly 15000 villages, though generally randomly generated and not that unique, and a general population of 750K in a land of 65000+ sq mi. Comparatively Skyrim is about 15 sq mi.
I'd guess the population is in the 20,000-40.000 range due to size an much space in the region generally sparsely populated
yeah I know, it was practically impossible to travel without fast travel. You could try your luck in the wilderness but you might just get fed up after the 2 day's run and still found like nothing.
Now lore wise in the population. We have around the basis of +/-500 men and women, depending on their loss from the snow elves. Also now we have to take in consideration of other Atmoran Refugee. Also deaths and births per a season/year/month or whatever. Then there has to be some sort of supporting evidence. There's also been a war recently, with both sides having "countless loses" and that could explain the missing population somehow, and the missing houses? Well they could have been disassembled for timber, iron and whatever materials. I just know I'm tired, and would agree that your 20,000-40,000 is closest to being correct.
One thing though, if they ever decide to make a Elder scrolls based in hammerfell, the Alik'r Desert must not be just one small, pitiful excuse for a desert. Also I haven't played TESO, which I don't count as a proper Elder scrolls game, and if the Alik'r Desert is featured in there I just hope it's big, and filled with caves, secrets, weapons and all sorts of fun stuff.