They (other than the cops investigating actual crimes against actual children) don't care about the children. They care about control. AI "CSAM" in particular (combined with deepfakes of adults made without the model's permission) is an emotional justification for more control in the form of draconian internet censorship and other preemptive measures.

Decades of megacorporation propaganda have paid off, and a fair portion of gen-z/y/x is hypervigilant about use without permission, even if the use is transformative and doesn't displace the original work. Their misguided concerns will play into the hands of the politicians seeking more control.

And it will do very little to prevent the spread of AI "CSAM"[1]. What are they going to do, regulate GPUs or any AI training software?

[1] Or any of the other concerns of today, like voice cloning or mimicry of personal likeness, like what just happened with Taylor Swift. The cat's out of the bag for images; OSS voice cloning is roughly at elevenlabs' quality, and it'll be surprising if there aren't, very soon, easy-to-use interfaces for voice cloning and tts.