Does reincarnation make antinatalism ultimately fruitless in trying to prevent (and end) suffering since existence happens regardless?

Just to clarify, I'm not talking about being personally childfree. Antinatalism views that procreation entirely is immoral, with the reasoning being that it forces a being into a world of suffering. It uses the asymmetry argument of suffering vs pleasure, with pleasure=good, suffering=bad, no suffering=good, no pleasure=not bad unless if one feels deprived. So, it insists that being nonexistent is most ideal since there's no suffering nor feeling deprived of pleasure.

However, this assumes that our consciousness was nonexistent until a very specific set of parents procreated (which even as a man bitter of life itself, I find this raises too many questions, like why wasn't my first-person awareness in the first life form or any of the ones before this vessel? What makes this body special enough for my "one and only" awareness to manifest under?). With reincarnation, we move from life to life. This would imply that even if our parents did not procreate, our consiousness would still manifest under a different set of parents. There's also the belief that there are an infinite number of realities, so even if everyone here stopped procreating or even became extinct, life finds a way.

Mind you, this isn't to say that we should recklessly procreate. I firmly believe that if a life were to be brought into this world, it should be under ideal circumstances like a good community, good parents, plentiful resources, an optimistic life plan, etc. I also insist that people should prioritize adoption as there are existing souls here that need help (again, there are an endless number of realities, so our hypothetical children can go elsewhere). But in terms of trying to prevent suffering by not procreating, I find that reincarnation renders antinatalism's goal fruitless.

But what's your take?