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?
If you expect a this for that that benefits the giver. Like say a pharma offering free airfare and lodging to a medical conference if you talk up their product to patients.
There will be corner cases, obscure circumstances, unforeseen loopholes, etc., but this would be a good start.