According to what I've read, the Army POW/MIA operation (which does this) has only a limited budget which it has chosen to devote to recent serviceperson bodies. There is an interesting article on this
https://www.staradvertiser.com/2018...-war-soldiers-without-conducting-dna-testing/ regarding the reburial of 2 ACW men who may have had New England connections.
Body retrieval for DNA testing would be pretty expensive. Someone who could afford to do it privately might be hard pressed to find a suspected body except by serendipity (or as noted in the article above). I found a number of the soldiers that I studied have what is called "effigy graves" (that is, the gravestones are really memorials to a soldier whose body is actually not there). Unless they've had research done, I suspect that most of the families don't realize that there is no body there.