I'm sure that one of scribes that count average human lifespan sees lots of age 0 that ruins the calculation and realize that the 'average human lifespan' will not be worth it, or at least misleading. Why don't they use another method or exclude the child mortality (or whatever outiler data)?
This is a good question. Whenever I hear a historian talk about ancient lifespans they mention that if you survived to adulthood it wasn't that different.
What do the statistics really look like when you stop accounting for massive infant mortality?
So I'm not sure who you mean when you talk about scribes. Accurate life expectancy numbers require (at their simplest) averaging the age at death for everyone born at a certain time; to estimate life expectancy in a cohort that's still alive, you need access to detailed statistics about a population, including age-specific mortality rates. As you can imagine, given the data collection infrastructure and the mathematical tools necessary, we don't really get good life expectancy data until the mid-19th century. No one prior to this was calculating life expectancy, or likely would have thought in those terms.
We do have historical life expectancy calculations, but they come through either secular or religious records that were collected for other purposes (think temple records in Japan, or the Bills of Mortality in London). Life expectancy for other populations -- such as ancient populations -- are based on pretty sketchy estimates, though the best we can do. They are based on grave inscriptions, burial sites, or historical data giving ages. Take a look at this table from the Royal Society of Medicine and you will see how small some of those n's are for historical estimates.
In regards to the second part of your question, modern epidemiologists do use plenty of other methods to exclude child mortality; routinely reported are life expectancy at 5,15, and 65 years, which you can find easily. Historical samples will also attempt to calculate these. Notably, looking at good data, even when you exlcude childhood mortality, life expectancy has been increasing. I'd actually argue that there are much better ways to visualize the age of a population than life expectancy measures -- a population pyramid gives a wonderful snapshot in time. There have also been attempts to calculate these for ancient societies as well, which you can find.
Hope that helps! Biostats isn't my specialty, but I love this stuff.