Take the books with you, text with your friends,..
This is how I solve problems now, why should it be any different at school?
Why should I solve the problems on my own, when I can rely on the experience of my peers and they on mine?
The problems you are trying to solve are mostly about finding a solution to the problem. Exams are mostly about trying to find an objective measure by which the pupil can be judged.
If you come up with twenty exam-level questions and give them to two million students who are allowed to collaborate, chances are, you'll get twenty answers that are correct. But what you won't have is a way of being able to distinguish who was able to work out the answers from others who merely copied the answers from a forum dedicated to helping with the site.
Worse still, you'd get parents "helping" their kids during the exam if they're allowed the cheat. Clever parents would just help the kids directly. Rich parents would help their kids by outsourcing to clever professionals. And poor/stupid parents - well, their kids would probably fail the exam.
The only way to really rectify this is rather than letting the students "cheat", you let them have passive access to online reference material such as wikipedia. But the problem here is that the Internet is always a two-way street. The very act of performing a search, for example, is an act that is sending information to the Internet. This means that effectively locking down the exam so that pupils can use the Internet but can't send the questions off to be answered by their rich/clever parents is impractical.