Earlier quoted context omitted.
Shouldn't prosecutors prove that it was you and not someone else?
"Should", yes. (Details obviously depend on jurisdiction) For that, they get a warrant to search your home and for your computers to be confiscated to do the forensic analysis on them. You might get them back after a few years if nothing can be proven. They also might tie you into it for knowingly supporting it by installing such a VPN, some places make you responsible for everything happening through your connection…
I mean, ISPs do this don't they? Telephone networks do this don't they?