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?
There would be no commercial ads online if google received no kickbacks to show ads. There would be no influencers, either. I'd be okay with non-profits and government agencies advertising benevolent things to us, like vaccinations.
The only hard part is to develop systems to actually ensure nobody is receiving compensation if they are showing a product.
I'd also be fine to make exceptions for internal advertising, e.g. you're already on the Google website and Google is advertising their own products/services to you.