It’s equally possible that there was more than one or even a day where only people were born and no one died.
There was a low point where only about 2,000 humans were estimated to be alive. Certainly you couldn’t have had someone dying everyday then
You’re right in general, but 1:50,000 implies an average lifespan of 137 years, unless I’m missing something. I think 1:15,000 is a more reasonable estimate.