My experience is that it is always important to criticize free speech absolutism, especially when people behave as if it were an atemporal concept. In reality, most of the world for most of the time has had various compromises between protecting individuals and society on one hand and free speech on the other.

That said, I think your take is also empirically supported. There is this [1] very interesting study which comes to the same conclusion. It uses broadcast range of radio towers to do a quantitative analysis on the potential effects and finds few. Interestingly enough, I have seen other studies with similar designs that do show persistent effects of exposure to broadcasts, so I’m favorable to the idea that this one really is a valid null finding.

[1] https://www.ushmm.org/m/pdfs/20100423-atrauss-rtlm-radio-hat...