The only way of knowing is after the fact, when the prompter has the knowledge to discern whether the answer is correct or not.
In which case why are we asking questions we already know the answer of, other than these are toys and fun?
I really wonder what happen when the novelty wears off in a few years, where these things are actually useful.
Humanity has developed few abilities to escape from ancient things like group think or propaganda (since long ago in the form of stories and unproven assertions about one's own group and others).
That may very well be because there is no advantage - having a cohesive group is more important than "seeing truth".
That would mean that there will be no adjustment in the future either. "Truth" does not appear to be all that important to survival and procreation I think.
This might be true in a strict sense, but I think it's really, really important to consider the uses of LLMs vs a high-school graduate. LLMs are confidently wrong (and confidently correct) with the exact same measure, and in many ways they are presented to users as unimpeachable.
If I ask an average person to do a medium-complex logic problem, my human brain discounts their answer because I've been socialized to believe that humans are bad at logic. I will take any answer I'm given with usually appropriate skepticism.
LLMs, on the other hand, are on the computer: an interface I've been socialized to believe is always correct on matters of math and logic. That's what it is, a logic machine. Second guessing the computer on matters of logic and arithmetic almost always result in me realizing my puny human mind has done something wrong.
To me, this directly contradicts your conclusion: LLMs are mostly only capable of misleading large portions of the population.