We have two legs, and so we tend to like rhythms which 'go into' two. We also tend to like tempos which match things we can do with our legs -- slower than a stroll hardly feels like a rhythm, faster than a sprint and we mentally recalibrate to half-tempo.
By the same token, there are lots of actions like scrubbing or sawing that are naturally fall into twos - back and forth.
I don't think it's right to point specifically at 'contemporary' music. Folk music and classical music are primarily in two-legged rhythms. 4/4 is the most common time signature, followed by 2/4.
At first glance, waltzes would appear to disprove my argument. But bars of 3/4 tend to come in pairs (One two three, Two two three.) so we're back to that walking rhythm. There are plenty of 'contemporary' songs in 3/4.
12/8 is more or less equivalent to 4/4 with triplets. 6/8 is more or less equivalent to 3/4. And so on.
The time signatures that don't fit into this are prime numbers higher than 3 - 5/4, 7/8. But these are rare in classical music, possibly more so than in contemporary art-rock, prog-rock and jazz.
Why is 4/4 more popular than 2/4? I'm not sure. Maybe that tiny bit of variety when scrubbing or sawing or marching or dancing is welcome.