Is it possible to find the parentage of an ancestor whose death record doesn't have parents listed?

Thomas Morton (1814-1873) is my fourth great-grandfather and he apparently was born and died in Belmont County, Ohio, USA.

Bizarrely enough there is absolutely no mention of his parents at all whatsoever on any genealogy site I have ever found him on. I also found his death record and his parentage was left blank on that too.

Why would this happen? Is it even remotely possible that I could ever learn who he was born to?

https://www.findagrave.com/memorial/220162046/thomas-morton