As for "GPT-4" fabricating things, I remember in school how I wrote essays and was given A's despite citing NYT and Wikipedia. Fabrications exist all over the place. If anything, hallucinations might give more examples as to how to be skeptical of any source and look for direct sources as much as possible.
"Actually it's good that AI sucks because it will teach people to be more skeptical" is not a very compelling argument.