> Is the problem actually "free?"

It's not. Paying to avoid advertising (which is the precursor to the modern "paying to avoid total surveillance") has been a thought-terminating marketing cliché since the days that "pay TV" was being introduced in the 60s. At this point, as you say, it just serves to blame the surveilled for the surveillance.

People using a free service make a lower-quality advertising target than people using a paid service, and people using a less-expensive service are a lower-quality advertising target than people using a more expensive service.