Maybe if we had been designed with three legs, the even time signatures of 2 and 4 wouldn't be so popular. 6 would possibly survive, especially in slow time! 5 time and 7 time remain rarities for much the same reason.
It's probably the fact that in 2 and 4 (and 6 if that gets counted in 2 lots of 3) literally evens everything out. Dancers will always be on the same foot at the same place in each bar, making the counting so much easier.
Historically, a lot of music was played for dancing, and there were several in 3 time, but most of that seems to have passed by. Of course, some songs start with words, and when they have music added, the 3 time becomes the natural rhythm to be in. But 4 time is the most common, by far - so much so, it's known as common time - although the 'C' as the time sig. does not represent the word 'common'.