It's not automatically given that the zero-to-negative population growth among post-industrial societies will be sufficient to mitigate the fact that the number of resources they use per capita can be an order of magnitude higher than pre-service economy societies.

Although I do agree that it does seem like getting everyone wealthy enough to snap out of high-birth-rate-mode as fast as possible is probably the best non-coercive solution for minimizing this sort of risk. (Which is actually part of the reason I speculate that effective altruism might be better placed in global intervention than in science research, though I remain uncertain)