When I read it some years ago, remember thinking Cornwell's book is one of the worst out there - and there are some contenders. It's almost a classic study in some sort of Captain Ahab folly - she becomes so focused on this theory, that the universe is bent to accommodate it.
Sickert's just an artist and JTR was part of the world in which he was operating. Artists reflect their worlds. He too, may have had an obsession with JTR (I keep writing "JRT" then have this image in my head of a murderous jack russell terrier).
As Cochise says, not enough hard data for us to ever know anything - a bit like some of the more compelling cases in our own lifetimes - and that is precisely why it is so compelling. FWIW, I think Kosminski is the strongest candidate (not that the shawl DNA thing convinces me of anything, but for other reasons) but I still think it's more likely that it's someone else entirely who isn't even a name on a census. Having spend a couple decades often chasing people who disappear in Victorian England without actually being dead. People who would never be findable unless you get lucky. 19thc cities are full of them and no place moreso than London.
(ETA: To clarify, my targets have been people more like the victims, than JRT - women whose lives fell apart, and then had to vanish into the anonynmity of a city with a fake name, and I've seen a surprising number of them. They never turn up again. Not even in death records, or rather, not under their birth/married names).