Nice try but normally modern forensic evidence doesn't work that way. They found (140 years old!) mitochondrial DNA of a Polish barber named Aaron Kosminski on Catherine Eddowes' shawl. Catherine was a casual prostitute and Kosminski was known for visiting prostitutes...
Imagine that police enters your house and arrest you. Why? Because you visited a club the same night. While dancing you sneezed and some nasal fluid ended up on the shirt of the dancing girl next to you. Later she got killed and police found the DNA of the girl and your DNA on her shirt, but for some reason no other DNA. Did you kill that girl?
There are many theories about Jack the Ripper's identity. For example:
- Jack the Ripper was an aristocrat and it was never planned to arrest him.
- Jack the Ripper was an artist named Walter Sickert.
- Jack the Ripper was a member of an occult lodge and the victims were human sacrifices.
- Jack the Ripper was a member of Scotland Yard because he knew the patrol routes and patrol times of the policemen.
- Jack the Ripper was a traveller. He didn't stop killing, he just left the country. AFAIK no one really checked if there were similar international unsolved murder cases after the Whitechapel murders.
- The killings stopped because Jack the Ripper died of syphilis in November 1888. That might be the reason why he killed only prostitutes (revenge). In the final stage (tertiary syphillis) syphillis can damage the brain. That would explain why he totally freaked out when he killed Mary Jane Kelly, his last official victim. A few days or weeks after that murder, Jack the Ripper would be already buried. It could be interesting to check who died of syphilis shortly after November 9, 1988 in London.