The problem with describing it in terms of cost-effectiveness is that you now have to put a price on how much we can justify spending on child sex trafficking. What is that number? How much is too much to save a child? How can you possibly answer that in a satisfying way?
>It's possible that there are cost effective things we could do that we're not currently doing, but those things tend to be uncontroversial, so when someone uncovers one it generally does actually get enacted and becomes the status quo. That's the issue: Name any given thing you suppose we should do instead of Chat Control. Enact it, as many of them already have been. Tomorrow they propose Chat Control again, so what now? Offering and even enacting an alternative hasn't satisfied them, they keep trying to pass it anyway.
>What are you supposed to do when you've not only offered solutions but enacted and implemented them already and your opponent is a fear monger who will never be satisfied because they have an ulterior motive for their dangerous and ineffective proposal?
The proposal up-thread seems like a good place to start. If we believe that these tech companies have through their software and platforms made it easier to exploit children, that justifies taxing them to offset the negative externalities they create. We then take that money and use it to increase funding for investigation and enforcement. I have no idea if that will work, but it at least puts the people you view as the enemy on the defensive and gives you the chance to win some of their supporters back to your side. Because right now you're letting those fearmongers dictate the terms of this political debate and their persistence on this issue shows you aren't making any progress in changing that.