Your conclusion is based upon an assumption that we need more humans to progress as society. If AI develops to the point where it is better as a partner than a human being, it likely means that we have achieved, or are very close to achieving labor post scarcity (the assumption being that an AI capable of achieving this is capable enough to do most/all human work).
When we achieve labor post scarcity, the number of humans has nothing to do with progress. Therefore, falling birthrates won't have any negative effect on progress.
When we achieve labor post scarcity in the medical field, life expectancy would increase, with us achieving biological immortality at a certain point. This means, that death rates also go down.
Considering the above, I thought you were referring to "dating and fucking AI partners" as the end of human progress (presumably because of a lack of any motivation to cause any more development). That's what my reply was talking about.
It's partially a joke made out of fear. A nuclear power is at war with a country in Europe right now. Other nuclear powers are actively supporting the defense of the attacked country. Another nuclear power is very likely to launch its own offensive against a little island it claims is it's this decade. Politicians parroting fascist talking points are gaining power all around the world. You can see the cause for the fear, no?