The thing is, you can't just censor it away until it's gone.

To play devil's advocate for a moment: how do we know that?

I'm guessing you and I are both liberally inclined in our politics from the very fact that we're having this conversation. Probably we are both naturally sceptical of any form of censorship.

However, objectively, it is clear that some children really are being exploited in horrible ways to produce the kind of material that we sometimes hear about in the news. If a responsibly operated system for limiting its distribution could have a significant actual benefit in terms of reducing the incentive to create that material in the first place, I don't think a principled "absolutely no censorship allowed" argument is sufficiently powerful to dismiss the alternative out-of-hand.

To make these kinds of policies, I think you have to look at the big picture, and the merits of both positions, and ideally hard evidence about the likely outcomes of each outcome. Even then, you are almost always choosing the least of evils in such a situation, because there will be real and legitimate concerns about any policy you might finally adopt.

It doesn't fight the root of the cause and in the long run will only hurt the society as a whole.

I am absolutely in favour of going after the root cause of abuses, or any other criminal activity. But when you're talking about legislation and law enforcement, I think you have to take a pragmatic view and accept that you aren't going to be able to protect every vulnerable person overnight by magically eliminating all sources of evil in the world, no matter how noble your intentions.

If a responsibly operated system for limiting the distribution of things like child pornography can reduce the amount of exploitation going on in the meantime, at a direct cost in terms of limiting the freedom of expression of those who would distribute such material and an indirect cost of requiring a technical mechanism for censorship and the risk of that mechanism being abused for other purposes, I think it is still reasonable to consider it.

Then again, I also have strong views on the need for accountability in public office. In particular, I believe that betrayal of the public should be considered a high crime. If you're going to give that much trust to anyone then the penalties for abusing that trust must be severe, and anyone who tried to censor other material using this sort of system should expect to be caught and should be facing significant jail time and a ban on holding public office. If any government isn't willing to accept that responsibility and transparency and oversight, then my view on whether they should be trusted with the kinds of system we're discussing swings sharply against them.

We all know that it doesn't matter how illegal something is; if it can be found, the person looking for it will find it.

No, we don't know that. This is my point.

Obstacles always bear the chance of making it worse for the wrong people.

Yes they do, and that is why those obstacles must have credible oversight to ensure they operate responsibly and severe penalties for anyone who abuses them. But that doesn't mean we shouldn't consider taking the chance anyway, depending on what is at stake.