So, I dug into this somewhat deeply, and it's true that there's some case law which would make an outright ban of commercial advertising difficult, however:
The law is pretty consistent about the idea that any paid endorsement has to be "truthful". And as we've learned more about sociology and advertising, we've realized that things like paid endorsements are fundamentally not truthful, because they are misleading the public to believe that some figure or trusted source (even if only at a subconscious level - which is still enough to change consumer behavior!) is in favor of a product or brand.
So maybe if you could argue that paid speech is inherently untruthful (which I believe that it is!), then you could make legal policy that bans paid speech complaint with the First Amendment! (caveat: I am not a lawyer, I am not a legal activist, etc)
Read Va Pharmacy vs Va Citizens Consumer Council to get a sense for how well you're going to fare with "paid speech is inherently untruthful". It's addressed directly!
The law is pretty consistent about the idea that any paid endorsement has to be "truthful". And as we've learned more about sociology and advertising, we've realized that things like paid endorsements are fundamentally not truthful, because they are misleading the public to believe that some figure or trusted source (even if only at a subconscious level - which is still enough to change consumer behavior!) is in favor of a product or brand.
So maybe if you could argue that paid speech is inherently untruthful (which I believe that it is!), then you could make legal policy that bans paid speech complaint with the First Amendment! (caveat: I am not a lawyer, I am not a legal activist, etc)