I dont think it would be the lab that ultimately paid for the test, rather the shawl owner. The shawl owner is the author of the book I believe. One more test of a suspects descendant may not be prohibative, but a few tests possibly would be - depending upon the financial health of the shawl owner.
Minor elective surgeries, but painful. She’s fine. 
We don’t know what the financial arrangements between Edwards and Louhelainen might be. It’s possible Edwards simply paid Louhelainen for the tests. It’s possible that Louhelainen was sufficiently intrigued by the case that he agreed to do the extraction and analysis pro bono. It’s possible that Edwards might have cut Louhelainen in for part of the profits for the book, which would of course call into question his objectivity (and could also perhaps jeopardize his ability to publish the research in a peer-reviewed journal due to conflict of interest).
I’ve worked closely with molecular biologists who analyze both mtDNA and nuclear DNA, and am a co-author on a number of papers with them. Based on what I know, I don’t think the cost of analysis is going to be a major factor in limiting the number of tests you can do these days.
Podcast interview with Louhelainen: BBC Sounds - BBC Inside Science - Available Episodes
Since you know what you are speaking off, what would be the point in testing other suspect’s descendents?
For one thing, to exclude them. As has been said, unlike a nuclear genome mtDNA is shared by more than one individual. While Louhelainen says that he found a “100% match” between Kosminski and his modern relative, without the technical data it’s not completely clear what he means by that. If he were in fact speaking of the entire mtDNA genome, it statistically suggests a common maternal ancestor within 5 generations. However, since this is statistical it’s possible for the ancestor to have been further back, or even to have a chance match. Louhelainen indicates that the mtDNA is of a type common in Russian Jews. Since several of the other suspects were from eastern Europe, they could conceivably also have been matches.
Thank you.
I believed that the results were unique to a family.
For that matter, there were several members of his immediate family in Whitechapel/Spitalfield. I like his brother Woolf as a better suspect, simply because Woolf is a better serial killer name than Aaron.
Nope, Aaron the Ripper just doesn’t cut it for me.
What kind of Jewish Mother would name her son Wolf? Obviously, that is the guy!
That, of course, depends on Wolf actually existing. It could be clearer.
Oo, look, it turns out the case may not actually be OMG SOLVED!!! after all. Who woulda thunk it.
Gasp. What a twist.
…
Not the Jewish guy.
Cool.
I think most of the participants in this thread had more or less decided that it was in no way proven, although not so much because we suspected laboratory or mathematical error but rather that, even if the science is correct, it still wouldn’t be ironclad proof that Kosminski was the murderer.