>ike availability of water, temperatures, etc. We should see a constant emergence of new life all the time. Why would that process stop,

Anything that's so agreeable to abiogenesis that life might spontaneously manifest, is actually pretty tasty for things already alive. They swoop in and eat it before it gets started. So, I suspect that even what the article says isn't that they both arose in the same place, but in different places separated by distance, time, and/or environmental barriers.