Yet, we are unable to train mice, birds or primates to tap out the beat to a song!
My theory is that all animals have extensive defense mechanisms to prevent motor entrainment to external stimuli, since that would make one very vulnerable. Therefore, they only exhibit entrainment during ritualized mating, etc.
Humans have evolved to let down our defenses, on occasion, to support social entrainment. Yet, it is still really hard to dance or appreciate music when we are uncomfortable or stressed.
One test of this theory would involve giving animals drugs like mdma to see if it helps them loosen up and appreciate the beat. It works with people, after all. But I suppose proposals like that would be taboo science. Or, perhaps it would be unethical to give chimps mdma?
[1] https://link.springer.com/article/10.3758/s13423-016-1013-x