Look, either your formula is accurate or it isn't. Either I am right or I am wrong. Either your faith in the forumula is justified or it isn't.
You lofted the forumula. I observed that it isn't accurate due to the examples given. You stated, "Yes but." Sorry, nice try.
If you want to model the global population, you need to use the parameters that are appropriate for the global population. If you wish to narrow down to a specific set of a population, then a set of parameters that are specific to that set of circumstances will apply.
The model is a biological model. It does not reflect the affect of extreme government policies. And the parameters can change for changes in technology. If I were to develop a cheap and efficient water purifier that could be distributed to all families in Calcutta, the population there would increase in a manner that could not be predicted with the old set of parameters. The population would increase until another factor limits population growth (such as food supplies). However, even a drastic change in technology will not affect the parameters too much. Likewise, if China decides to kill all children after the first one, the model will not reflect this.