Just ban all political ads.
But then you could also be running ads to push a public issue such as climate change independent of anyone's campaign.
How do you differentiate between the two?
So you can ban advertisements from political organizations, but if a third-party or the Russians start running misinformation ads on climate change and pro-life, the media won't exactly recognize it as a "non political advertisement" and leave off.
In the election of 2016, most of the misinformation was not directly initiated by the political candidates. Your suggestion wouldn't affect any of the misinformation spread in 2016.
Canada, Ireland, and the UK all do this with Party Political Broadcasts: