Like a car? Still full of fail.
This situation is a bit like the one with car owners not necessarily being the driver of the car when an offence is committed.
So the ISP sends a letter to the payer of the internet connection which says "Who visited site X on day X using your internet connection? Unless you fess up someone else, we will assume it was you"
Might be interesting when the internet belongs to a company who may or may not have sufficient logging in place to work out who it was. Hospital porter on nightshift downloads some tracks....using a PC which the night shift nursing staff left logged on. ISP says no internet for your hospital unless you give us a name to prosecute. Doesnt really work does it?
Illegal activity moves onto encrypted connections. Skype have demonstrated an encrypted peer to peer global network already. A hybrid of Skype and TOR would be the next step. A Darknet client, if you like.....
If you are the security team for a company, you might be able to retain control by only allowing whitelisted programs onto company PCs.
If you work for the surveillance state, then your options are more limited. If you let people run PCs they built themselves (Linux, etc) then there's little you can do to control how they access the darknet. Conclusion: governments will make private ownership of PCs illegal - you will only be able to rent a government approved internet access device. See 1984.
Tell me why this isnt where we will end up.....