A free press doesn't necessarily mean that the press can do whatever it wants, exactly like free speech doesn’t mean that you can say whatever you want whenever you want to. I think it’s fairly easy to set up some rules about political advertisement, we already do it for other stuff like alcohol, tobacco, porn etc. I’m not implying that we should ban the media from covering politics, it’s just the blatant advertisement on social media and television.

It is unfortunate that you believe that what you describe is "free speech" and a "free press". You are in fact arguing directly against free speech, and in favor of a scheme where the government is extensively involved in regulation on the content of speech and the opportunities by which it might be expressed. It would be less misleading (to yourself as well as to others) to admit this.

More specifically, you are arguing against the speech that that the US supreme court has specifically identified as "core political speech," which has been explicitly covered by the strongest legal protections, such that any limitations must withstand the strictest legal scrutiny. You are suggesting that treating it with the lesser protections afforded to commercial speech is something good for society, that it is consistent with current legal treatment of free speech, and is consistent with the ideals of freedom. None of these are true.

(Well, not in the US, anyway. In Europe, this is actually normal and consistent with the way that speech is normally treated. But Europe doesn't actually have or want free speech, notwithstanding any protests you may hear about the topic.)