I'd actually prefer that, too. Especially prescription medications: there have been awful studies about correlations between patients asking their doctor (as the ads say) and getting that specific Rx even when unnecessary.
I also don't know how to get there constitutionally without somehow differentiating advertising from speech (the Court has declined every opportunity, which should be obvious from the term of art "commercial speech") or relitigating Central Hudson. I also don't know whether yielding on the Constitution in cases like these compromises my values. See where I'm coming from? All it takes is one case of ignoring the First or Fourteenth in particular and getting away with establishing some bad precedent. That's a future that would concern me greatly.
I've seen some folks arguing for jailing fake news authors here on HN. Ignoring parts of our Constitution feels good to think about in order to address a squeaky wheel. The ramifications of where that steers the whole cart over potentially decades must be carefully studied, however, some amendments far more than others (the First being one of those).