That's a good idea, but it falls down the first time someone in the crowd starts downloading cp. Instead of having one, or a few, people being traced to their IP and investigated for cp, you now have 1,000 people under suspicion. You can protect users by ensuring that the box doesn't log any information about them, but then the box's admin is the one being held responsible.
At the moment I set up TOR and use Starpage.COM instead of Google. Auto-delete cookies after closing the tabs and actively remove ads and tracking JS from web pages with the help of a few browser extensions. It's not perfect, but it's above average for the moment.
You know how we could become anonymous? Just pipe the traffic of 1000 people through the same box, mix their searches and pages loaded in the same stream. Then send them on the clear net - they can't trace back who requested what. Hiding in the crowd, in plain sight.