Then you should be laughing your ass off while playing every single TES title. I don’t know why they write stuff and refuse to make it work the way they wrote it, but they do A LOT. The Khajiit you see is actualy not the most common version of the Khajiit in TES, the most common version looks a lot like bosmer with tattoos all over its face but noo we had to get the furry kitty one instead of the most common one that is suposed to be everywhere according to lore.
In the first two games, Khajiit's were the bosmer looking fellows that you described. Who'd want to play a bosmer who has tattoos instead of a human cat mix?
Also, Argonians, being the only beast race, were getting pretty lonely.
Edit: The only reason that's in the lore is because of the first two games, if they were cats from the start it wouldn't be in there. You can also pretend some of the Bosmer you see in Skyrim are actually Khajiit's.

