Is the right to pay others for speech necessary for free speech to exist? If so it is already non-existent. No functioning democracy allows judges or politicians to sell their speech to the highest bidder for example.
The difference is that advertising is extremely broad while bribing a judge or politician is extremely narrow (not to speak of conflicting with their professional remit)
It's relatively easy and sensible to ban very specific forms of paying for influence. But a ban on publishing your opinion in someone else's publication is extremely broad and obviously in violation of free speech. Free speech isn't defined as standing on a corner yelling at people.
I also think it's counterproductive. All influence seeking (both commercial and political) would be forced to move from overt advertising to covert infiltration of our communication.
Why should advertisement be different?