Shouldn't a different algorithm that adds a some sort of separate logic check be able to help tremendously?

You, in your "limited experience" pretty much exactly described the fix.

The problem is that most of the applications right now of LLMs are low hanging fruit because it's so new.

And those low hanging fruit examples are generally adverse to 2-10x the query cost in both time and speed just to fix things like jailbreaking or hallucinations, which is what multiple passes, especially with additional context lookups, would require.

But you very likely will see in the next 18 months multiple companies being thrown at exactly these kinds of scenarios with a focus for more business critical LLM integrations.

To put it in perspective, this is like people looking at AIM messenger back in the day and saying that the New York Times has nothing to worry about regarding the growth of social media.

We're still very much in the infancy of this technology in real world application, and because of that infancy, a lot of the issues present that aren't fixable inherent to the core product don't yet have mature secondary markets around fixing those shortcomings yet.

So far, yours was actually the most informed comment in this thread I've seen - well done!