Facebook ran an experiment in 2010 showing they can get out the vote via the news feed:
https://www.smithsonianmag.com/science-nature/how-a-facebook...
All an advertiser needs to do is have a way of targetting who they want to get out and vote, and get that to happen.
It seems at least possible this happened with the 2016 EU referendum in the UK, and was one of a bunch of factors which swung the result - Dominic Cummings, who ran one of the campaigns, certainly claims that it significantly helped (search for digital in https://beta.spectator.co.uk/article/dominic-cummings-how-th...).
I'm reasonably sure they were using ML to work out a set of factors for who voted which way on the referendum from other data (answers to the Euro football contest), then targetted ads at those factors. It was pretty clever.
"See how influential these ads can be! Someone in the GRU can pick the president by spending 100k on facebook ads."
It's self-serving like everything else these companies do. So they're willing to go in front of congress and do kabuki theater about how serious their position to influence people is and make guidelines---which they will undoubtedly ignore.
Crucially, we are exposed to political advertising from many different sides of the political spectrum. I regularly see both Bloomberg and Trump ads. The domain in which we see political advertising is not controlled by the advertisers themselves, so that is a fundamental difference from Google's influence.
It's the same story with money on elections. People were and are extremely paranoid about monied interests dominating elections, but we have seen Trump beat Hillary with half her money and now Bloomberg will inevitably drop out of the Democratic primary even though he is outspending everyone else combined.
People have far more agency than armchair psychologists and sociologists would like to believe.