I don't want that, but I see your point. I would rather our population have a healthy immune system where bad ideas just don't survive, than to have us live as Bubble Boy, cut off from the rest of the world forever.
Hell, even if it was adults given some training for self-control, the vast majority of them will dip into the sweets table from time to time.
People are really good at rationalization, such that even if they know up-front which choice was fake news and which was not, I bet you'd similarly observe a significant fraction (if not majority or super majority) of people choosing the fake news to feel better.
Sadly, I'm unaware of any real solutions to the fake news problem that don't make things even worse.