I agree there's some kind of recent trend here, but "body" has been used to mean "individual" for a long time. Here's an example from 1782:

https://en.wikipedia.org/wiki/Comin%27_Thro%27_the_Rye

I recall hearing somewhat archaic phrasing that something was "good for what ails a body", or some such. Specifically, I think it's an archaic southern-ism? Though you're right about the general trend.

What's the difference between, say, white people and black people? It is that the white people's bodies have pale skin - or "white" if you prefer - and that black people's bodies have dark skin - or, perhaps, "black". Any discussion of white people vs black people must, then, at heart, be somehow about their bodies. Because that's exactly what "white" and "black" refer to.

I assume the terminology is intended to deliberately draw one's attention to this.