They have done self-regulation when it comes to political advertising in the United States, but that's not flawless and, frankly, a lot of stuff falls through the cracks.
I actually think this should be on the influencers themselves. Just like when you're placing a political advertisement on TV, on radio or in print and you're required to say who paid for that political ad, the same should be true for content that's created and is seemingly authentic, individual-creator content being posted on social media.