You’re saying a lot of things here, but is one of them that an event could be detected far away because it’s old, or because it’s such a rare event that the chances it happens near us are vanishingly small?
These systems are very far away because you are looking more than 13 billion years back in time. The argument is JWST has a small field of view and these Pop III stars are like flashes in comparison to the age of the galaxy. So the probability of catching one that is bright enough to be detected is just super low. Which is why there is a strong prior that the HeII could be from other physics that is relatively well understood. But really the OIII emission is the biggest sign that this isn't a "primordial galaxy"
Pop 3 stars were formed in the very early universe and have been long gone. So there is no way for us to see the light they emitted without looking at the most distant galaxies.