Your speaking of time travel as if it's real and we know what the consequences of it would actually be.
In the original ending, they prevented Judgment Day but John still existed in the altered 2029. Sarah mentioned that even though Judgment Day was prevented she still has memories of the dark future that never came to be.
It's fiction. You establish your own set rules and then you make sure to follow them. Nowhere in any of the Terminator films is it established that a person would disappear out of thin air, if present day events are altered.
Here's another Cameron quote:
I asked myself a hypothetical question: what if you could you grab a line of history like it's a rope stretched between two points, and just pull it out of the way? If you can pull it just a little bit out of the way then cut it at that moment, maybe you could change it and history could go in a slightly different direction. Like the catastrophe theory. If you could actually do that you would get a future that no longer exists except in the memories of the people who are here now. They have a memory of a future that will never happen, which is curious, because it defies our Newtonian view of the world. But couldn't it be possible? That became my point of departure. It's like the Terminator is an anomaly of our time because he's the only one who has memories of a time that will never exist. His particular future does not exist anymore.