The real reason is that it's because that's how the ending is written.

A reason I've rationalised is that it's because the Prisoner is unique among the Strangers in that they don't seem fearful. When the Strangers realised what the Eye could do, that's when all the erasure started, and they shut themselves off into their fake home planet. Only the Prisoner wasn't afraid, and held on long enough to see if their efforts worked. And it did! The Nomai successfully received the Eye's signal and came to the solar system, and that was enough. The Prisoner could have blown out their lantern at any point, but waited in the hope that there would be some proof that their plan worked.