I don't think so rik. All they would need to do is force the users to sign a contract on sign up removing the stores liability. It would then be up to whoever was looking to uncover the person doing the crime. The coffee shop wouldn't need secure logins they would only require the flash of an id or clubcard or whatever. Anonymity is the main perk of an internet café.
They'd also have to log the MAC of every machine, and ensure it wasn't spoofed, surely? Otherwise, the lawyers would argue that in the absence of being able to prove innocence, you're guilty. I know the justice system is meant to work the other way round, but there are times when, in the UK at least, it doesn't.
It would literally be an end to private data. I don't think the UK has gotten that bad just yet.
Trust me, our lot are working hard towards that goal.