Ah, here's where we disagree.
Let's take a practical example: Why can't the providers perform metadata analysis on traffic externals, and identify significantly-sized closed groups of participants? The providers could then pass those clusters over to law enforcement to take a closer look. Most of the clusters would probably be nothing, or at least not meet the threshold to get a warrant for further investigation. Some of the clusters might have significant participants who are already on law enforcement's radar, but below the line for investigation.
This would be a definite infringement on overall privacy. It would also be a potential step towards improving the CSAM situation. It would not require client-side scanning.
I don't know how palatable this suggestion is. My point is, compromises are possible. This is just one example -- I'm sure there are others. The technology industry is not, I believe, currently actively seeking these compromises.
Failure to recognize this perpetuates the fundamental inconsistency.
Not true, you can have privacy and at the not tolerate child pornography, those are two perfectly compatible positions and arguably the current state. What you can not have - by definition - is privacy on the one hand and on the other hand no privacy in order to look for child pornography. You can still fight child pornography in any other way, but when it comes to privacy, you have to make a choice - give people their privacy or look through their stuff for illegal content, you can not have both. If you have enough evidence, a judge might even grant law enforcement the permission for privacy violating measures, it should just not be the default position that your privacy gets violated.