If that is the case, why stop at child pornography. Physical child abuse like beatings present a far greater threat in terms of children impacted, but we aren't discussing the wholesale monitoring of every adult with a child, are we? Are the children that are victims of physical abuse not deserving of the same attention we give to those that are victims of sexual abuse?
There are alternatives that mitigate the problem without centralized government involvement and dragnet surveillance. Opting for a law enforcement-based government solution from day one pretty much eliminates all creative thinking on how the damages from child pornography can be reduced to acceptable levels.
I emphasize acceptable levels, because the correction of all ills and dangers carries with it diminishing returns. If you want to completely eradicate something, it's going to cost you an order of magnitude more to eliminate the last 20% of the problem than the first 80%. Costs here a both financial and freedom-wise. The in both time and freedoms for services (telecoms, etc.) and places (homes, offices, etc.) is good enough for probably 80% of the benefit. Beyond that the cost is just too high for too little benefit.
You can also get 80% of the benefit by just identifying the small subset of children that present the highest at risk group and providing special services for the monitoring and social support for that group. No need to drag in the rest of society.
First, child pornography itself isn't really the problem, but the problem we focus on because its visible and elicits emotions. We focus on the end product, but the root problem is how child pornography is made. Child porn doesn't only exist in electronic form. Getting convictions of users of child porn isn't going to protect any children. We know undeniably that a market exists. Going after the buy-side is never going to have a meaningful impact, because there are a lot more buyers than creators and the amount of effort to bag a few consumers here and there is a drop in the bucket and will never be sufficient to reduce demand enough that there isn't incentive for the supply side to keep producing it. If you make it harder, then the price just go up. Profits don't change.
Personally, I would like us make the consumption of child pornography legal but keep it illegal to manufacture or distribute child pornography. By keeping the buy side legal, you gain enormous amounts of visibility into the market dynamics that don't exist, when you force both sides to go underground making observation difficult enough that the privacy of many innocent people needs to be compromised to make policing even marginally effective. Furthermore, it would still be considered taboo and a sickness and we'd encourage purveyors of child porn to seek psychiatric care, where we would counsel them on their addiction and show them the damages caused by their consumption. To get access to free psychiatric care, we can solicit cooperation from the buy side in discovering who is operating on the sell side. This removes a lot of trust in that market, because instead of both sides being driven to trust one another for fear from prosecution of the same law enforcement entity, the sell side will end up with a healthy mistrust of their customers.
The fastest way to destroy a market is to destroy trust in that market. TBH, I'm surprised we don't really spend any attention on how you effectively undermine markets like we spend time on how to foster liquidity in markets and making them more efficient.