Earlier quoted context omitted.
"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…
Why can't anyone who join be incorporated as a utilities provider, and shed the responsibility of monitoring the traffic (and the legality of it) to the initiator of said traffic? I mean, ISPs do this don't they? Telephone networks do this don't they?
This is the tradeoff when registering an ISP in the jurisdictions I'm familiar with: you are immune to legal action concerning the data that is carried over your network (ie. you won't get raided for a customer sending death threats), but in return you must cooperate with the authorities and provide data on your offending customers. You must do whatever is necessary to be able to provide this data upon a subpoena: from assigning static IP addresses / CGNAT port ranges to customers, to logging every NAT translation from your roaming mobile network.
Source/background: operating an ISP in Poland.