Your reference to a differential approach, at least, brings light to the origin of the formulation as it politically justifies the approximation.
But I do not agree totally with your approach.
It is true, provided that the mortality is the same that the differential equation will be
(population / 15) * dt as the limit of the difference equation if the time step is decreasing to 0.
But the equation (population * (1 – (mortality * time step)) / 15) is right too even in the differential equation and has the advantage to be right too in the difference equation where the time step is larger.
But if you stick to the extreme hypothesis that all people die in a time step, you cannot erase the mortality * dt because the mortality is equal to 1/dt and the term with mortality is no more marginal compared with the other terms. In this case the error is increasing as the time step is decreasing.
I prefer a formulation that is always right, even if slightly more complex, whatever the time step and the formulation (difference or differential).
I do not totally agree when you write.
<Certainly if mortality is 2/year then the appropriate solution interval is at most 1/8 and probably better 1/16 or <1/32.
I think that if mortality is 2/year during a semester then the appropriate solution interval is at most the smaller possible taken into account the software used, with the original formulation, because it is difficult to evaluate the effect of the integration error on the rest of the model, unless one has done the appropriate sensibility analysis. Why not just use the correct formulation without having to bother about eventual marginal effects generated by the approximations?
I am not ready to sacrifice exactitude for a vague notion of conceptual clarity that is only understandable for people with notions of calculus. I do not think either that the formulation is odd unless one is sure that what you name numerical oddities do not affect the objectives of the model.
The proposed formulation is approximately right with a very small time step, conceptually right with a differential equation, but neither approximately nor conceptually with bigger time steps as those used in SD.
I respect your approach, but I am more interested with very pragmatic approaches, even if they look less conceptually interesting. Finally what counts is the usefulness of the model. Is the world3 model effectively used by people and implemented?