That is assuming both sides are equally fervent and vocal in their beliefs, which is rarely the case.
Usually you have one side with documents/evidence, and opposing them another side without documents/evidence who have nothing more than a fervent belief that there is a conspiracy, the evidence is forged, that they are being lied to etc despite all evidence to the contrary. Of the two sides, which one do you think is more likely to petition Google for the removal of information from their search engine?
Let me illustrate this with a real world example. If you visit any average forum for any product or service, you are likely to find posts by unhappy customers there vastly outnumbering posts by happy customers. This creates the impression on any casual visitor that the product/service is bad. However, this is usually untrue- it is simply because happy customers go on with their lives whereas the angry ones are motivated to telegraph their anger far and wide.
By the same token, allowing arbitrary removal of information is likely to hand over control of the conversation to those who are the most fanatic, the most dedicated and the most vocal irrespective of the actual merits of their beliefs.