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.

I want more transparency, not less.

That surely depends heavily on your definition of functioning democracy.