This begs the question: how could you reliably distinguish advertising from other forms of free speech? 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 sample…
We don't need to go into absurd discussions in order to prevent 99% of the harm that comes from modern advertising. The line is clear: is money being exchanged in order to promote a product? That's advertising. Someone I know mentioning a product because they want to recommend it to me? Not advertising. Giving out "free" samples? Presumably someone is being paid to do that, so advertising. We can later quibble about…
So if I paint my store front's sign myself, I'm good, but if I pay a signwriter to paint it, it's illegal?
I guess I better become "friends" with a signwriter, so that they don't mind making a sign or two for me "for free". And so that I don't mind giving them a widget or two from my store sometime in the future.