"Maybe we need to start culturing and DNA testing cancers." I assure you this is being done at a massive scale.
Due to cellular stress, cancer cells disobey multi-cellular governance. They behave more like independent organisms fighting for survival, reverting to primal programming.
I was trying to remember which mammal in Australia gets tumors from fighting, and I found a reference to a mother getting melanoma from her daughter. It’s unclear to me whether the cancer transmission was rare or the identification is rare.
Transmission of cancer is rare in humans—if it were not, it would make someone’s career to find many cases of it. While we can’t say that all sheep are white, we’ve looked at enough of them to say that black sheep are not common. Furthermore, it’s very clear how the Tasmanian devil cancer is spread—it’s around the mouth while they are biting each others faces; it’s not as obvious how one would spread most human cancers.