The courts already distinguish "commercial speech" as a class of speech. Would we prevent all forms of commercial speech? What about a waiter asking you "would you like to try a rosé with that dish? It pairs very well together." Is that "advertising" that would need to be outlawed?
What about giving out free samples? Is that advertising, and thus should be illegal?
What about putting a sign up on your business that says the business name? Is that advertising?
I hate advertising and propaganda. But the hard part IMO is drawing the line. Where's the line?
So lets do this: ban all ads in print, video, and in-public. Make the fine so high that you’re going to have to declare bankruptcy and close up shop. Or just straight up revoke corporate charters. There’s your line. I’m happy to start here and negotiate backwards. But this needs to be in effect while we work it out. Advertising is killing us. I don’t need or want myself or my family constantly assaulted by ads.
Finally, to be frank I find advertisements a sibling of propaganda. I don’t want either.
There are dangerous consequences to handing the government the authority to ban public communication (even about mouthwash brands) without very careful scrutiny.
Imagine if you couldn't advertise energy alternatives because oil and gas came first and, with advertising banned, we can't even talk about the relative merits of installing solar vs. buying coal-made grid electricity. The status quo will maintain until the planet cooks.