Many of The Doctor's companions are not contemporary humans. From the beginning, Susan was Galifreyan. More recently, Jack was born in the 51st century. In between, we had Vicki, Steven, Katarina, Sara Kingdom, Jamie, Victoria, Zoe, Leela, the various incarnations of K9, Romana, Adric, Nyssa, Kamelion, and Turlough. Many of the companions in other media also fit the bill, a handful of whom were made in-arguably cannon in Night of The Doctor. The almost or non-human and/or non-contemporary companions are in the minority, but it is a significant minority.
That said, out of universe, a significant role of the companions is to bridge the viewer's world to The Doctor's. Writer after writer has used the current companion to ask "What is it, Doctor?" It is easier to frame this question in a time and place useful for exposition if the companion asking the question shares a frame of reference with the viewer. Contemporary episodes save on set construction without having to overuse the local rock quarries. It hasn't hurt the ratings to have eye candy on the show, either.
In universe, Earth seems to be his favorite planet, and contemporary humans stick our noses where they don't belong, i.e., The Tardis.