If you leave the dealership with your new vehicle, and decide to go run over 10 people, the dealer is not on the hook for your actions.
Same with gun stores not being held liable for gun owners.
There may be background checks in place to ensure they aren't selling a car to someone that can't drive (Driver's license) or to make sure someone can own a gun (Background check), but once you pass the initial screening you are on your own for liability.
Political ads should be the same, basic KYC to verify the person buying the ad is who they say they are or allowed to represent an entity, but beyond that anything they want say let them say it, let the public scrutinize it, and let their ideas be debated.
I could see a world of hurt if this was completely unregulated, as in anyone could pretend to be anyone and buy an ad any which way without verification. This would lead to an insane amount of slander/mudslinging.
Just my 2 cents, probably not worth a penny.