[SunkenCiv]

He doesn't because the DNA study was botched, not least because there is no reason to believe she ever wore the shawl. The supposed DNA match turned out to be a typo, because the work was so incompetent.

May as well test DNA from all the supposed Ripper letters -- even the handwriting doesn't match, apparently they have about as many authors as there are letters, which is a little disquieting.

Last I knew, Scotland Yard wouldn't release the names of the various informants from the nearly 140 year old investigation, claiming it could endanger lives. That's good and nuts.

[CommerceComet]

Didn't The Journal of Forensic Science publish a DNA study in 2019 that reported that there was a DNA match of both Catherine Eddowes and Aaron Kosminski on the shawl? I don't know about the robustness of the results but that at least suggests it was her shawl and puts Kosminski in proximity to Eddowes. (Of course, there are chain of custody issues all over the place.)

The results are more suggestive than conclusive and the original results were vastly oversold (as is always the case with any new Ripper theory) but after 130 years, it is doubtful that any smoking gun is going to emerge. This might be as close as we will get.