Campaign finance is illegal in most of the first world. If political ads were banned in the US, politicians wouldn't need money to get reelected (Ads get the majority of votes.). When a politician needs money to get reelected they have to take money from lobbyists.
Banning political ads is crucial linchpin to getting money out of politics.
There was a campaign finance law in 1971 that went all the way to the US Supreme Court. In Buckley v. Valeo, the US Supreme Court ruled that campaign finance laws are freedom of speech, in that without such laws, the every day person is restricted from being heard when the wealthy are allowed to use money beyond what the common person can pay. Because of this, the court upheld limits on contributions to candidates ruling campaign finance is legal, as long as it is limited to an amount everyone can participate in.
From the Supreme Court: "The Court affirmed a First Amendment interest in spending money to facilitate campaign speech, writing, "A restriction on the amount of money a person or group can spend on political communication during a campaign necessarily reduces the quantity of expression by restricting the number of issues discussed, the depth of their exploration, and the size of the audience reached." Further, the law's "$1,000 ceiling on spending 'relative to a clearly identified candidate,' would appear to exclude all citizens and groups except candidates, political parties, and the institutional press from any significant use of the most effective modes of communication."
The Court upheld limits on contributions to candidates.
edit: In 2002 there was another campaign finance law that went to the Supreme Court, again for freedom of speech. In McConnell v. FEC, the court ruled, "the need to control corruption overshadowes any minor threat to free speech".
Neither of those have to do with someone putting $500 down to run a political ad on Facebook. Local politicians, mayors, etc run political ads. Good luck policing all of that. If you block an individual from spending $500 on Facebook ads because of some law, you are violating that person's freedom of speech. That is entirely separate from campaign finance. Why stop there? Why not limit what Newspapers can say? They often get stories about politicians wrong, sometimes even in an effort to sway public opinion.
Banning political ads is crucial linchpin to getting money out of politics.