probably something to do with:
A. nobody trusts them (with good reason)
B. they really aren't suited to the colder climate
C. they originate from a client state of the thalmor (which is because they believe the thalmor brought back the moons, which is the very basis of khajiit society, biology and religion)
D. their most lucrative trade is moonsugar/skooma, which is illegal and watered down in skyrim
really, the question is why would a khajiit WANT to live in skyrim?
A. None of the races can be fully trusted then. Why would an average Nord trust an Altmer more than a Khajiit?
B. Yet quite a large number of Khajiit caravaneers not only live in Skyrim, but even sleep in tents during snowstorms while Nords with all their innate cold resistance got warm houses. Despite the cold climate, there ARE Khajiiti in Skyrim, just not in cities, but wandering around in cold weather.
C. Which opens up various RP paths, such as maybe someone's Khajiit has fled from Thalmor reigned Elsweyr, or someone's Khajiit has never even been in Elsweyr to begin with, and someone else's Khajiit could be a Thalmor agent, but so could be anyone, like the Altmer merchant Niranye in Windhelm.
D. Yet I've encountered skooma dealers of all races, also I recall doing some quests that involve skooma dealers, and none of them are Khajiiti. Also, is skooma really so illegal in Skyrim? Because I can freely sell skooma to any merchant in Skyrim (and then buy it back), unlike in Morrowind where even having it in inventory made things rather problematic.
Bottom line - I can't see how total lack of Khajiiti in cities can be justified lorewise. Fewer in numbers, sure, but none? Doesn't make sense.