About making the online thing safer

I have been wondering if it’s a very fool idea to think that many of the problems and crimes online could be lessened by forcing any user to give the real personal identification, other way, they are not allowed to have internet.
Is it very stupid or impossible? I ask from a vague idea about how this stuff works.

I see how many times, the police struggles a lot to find a person behind an online user, for instance.