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 I enter your restaurant, car dealership, etc. then you can pitch & try to up-sell your goods and services to me.
If I drive down a motorway or use your website, third-parties can't advertise their goods and services at me from spots you've sold them. (But you can tell me it will be faster to exit onto your toll road or that I should buy or upgrade my membership plan on the site.)