This is a long way to say you don’t have the votes. Airwaves affect turnout. They don’t flip people on positions.
They absolutely do. On September 12, 2001, ~nobody in the United States was interested in starting a war with Iraq.
Two years of propaganda later, and all of a sudden, half the population had acquired keen geopolitical insights which necessitated an invasion and occupation of a country that had exactly fuck-all to do with 9/11.
A decade later, all of a sudden, nobody wanted to fess up to wanting anything to do with that mess.
Public wants aren't discovered in some interference-free democratic vacuum. The people who own the press put a millstone on their side of the scales.
There was desire for vengeance on 12 September. Reporting and politicians channeled it. That’s very different from driving consensus against something people would otherwise support.
It works the same way in other countries too. Look at any country that you believe to believe in insane shit - most of those beliefs aren't organic.
Neither are the insane things you believe in. It's just that you can't even see that they aren't the product of your own reasoning. Fish don't have a word for water.