I guess what I am trying to say is that the population doesn't care. If you want to convince politicians, you have to convince the population.
IMHO there are valid arguments against ChatControl that are not "you see what you allow TooBigTech to do to you? Well with ChatControl you would allow much less to the government. Isn't that terrible?"
A strong argument against ChatControl, IMO, is that it builds a powerful tool of surveillance. Not because "someone fairly random will see false positives", but because someone in power (e.g. a president) could abuse it to maintain their power (e.g. by targetting political opponents).