Any solution that’s ineffective unless 100% of the population is morally upright is unusable.
Any group will contain defectors — cheaters who use the letter of the law against the spirit of the law, and will break the letter of the law too if nobody’s looking. (This isn’t necessarily a bad thing, but it’s a problem when these defectors also lack empathy or morality.) You can’t identify and eliminate these people — for one thing, the ethics of that are pretty muddy, and for another, their main talent is passing as morally upstanding — so any strategy for disincentivising a behavior needs to operate at least in part by making such people fight amongst themselves and prevent each other from engaging in whatever behavior you want to disincentivize. (This is why shame is such a powerful tool: it allows anyone to elevate their status over anyone else so long as that person engages in (or can be made to seem to engage in) some behavior that’s more or less globally accepted as undesirable in the community, so even very morally reprehensible people will shame in a prosocial way because it gives them an advantage.)
The thing about fake news is that it’s potentially pretty powerful. (It’s also a really vague term, but the variety of fake news that people are concerned about is specifically what’s normally called “disinformation” — mixtures of true and false statements crafted into a narrative designed to cause a specific targetted group of people to engage in some specific behavior. We’re not particularly concerned about staged photos of rats riding crocodiles, or press releases regarding dog brothels, or clear satire, or reports on the recent exploits of Bat Boy, even though all of these things are also fake news.) Anyone who wants to wield power will use the tools at their disposal, and the fact that media has become a very inexpensive tool to wield is probably a good thing since the kind of people who would use it to consolidate power are more likely to fight each other than to collude.
However, the real power of this kind of fake news is that people spread it because they want it to be true, even if a very small amount of effort would show that it’s false. This is not an accident: disinformation is engineered specifically to appeal to the target audience, so that it spreads.
I would argue that the best way to slow the spread of disinformation & rob it of its power is to educate people specifically to be significantly more skeptical of anything they want to believe (or that fits with their world-view) than of things that do not. In a media landscape that is in competition with its users, we must reverse Sagan’s maxim: that which is easy to believe (ordinary claims) needs more proof, because what constitutes ordinary has been taken into account (and sometimes engineered) when constructing false messages. At the very least, we must distinguish clearly between claims that are easy to believe for emotional or narrative reasons versus claims that are easy to believe for reasons related to the hard sciences.
A major flaw in humans is that believing is seeing instead of the other way around: we see evidence of what we believe, and anything that really violates our mental models is mostly invisible. We only see things that we’re looking for, most of the time. This vulnerability is well-known, and all con artists from minor to major take advantage of it. It can be battled with habit.