I get why one would desire regulation like this, indeed there's a bit of con-artist problem in the influencer space. But I think fucking with first amendment issues is a bit dangerous, especially now.
I think a better idea is to fight fire with fire. Call out the charlatans using social media instead of giving the government power to determine what is and isn't reality.
"Well, thanks to the Internet, I'm now bored with sex."
- Philip J. Fry