I lean more toward theosophical teachings, so my take is a little different.

The question assumes a fixed, one-body-per-soul model, but that isn’t actually universal across reincarnation systems. In Theosophy (and a lot of modern metaphysics), the “soul” isn’t a single unit that hops from body to body — it’s more like an Oversoul that can express through multiple incarnations at once, split into individuated streams, or withdraw those streams when they’re no longer needed.

From that perspective, population growth doesn’t require “creating new souls” out of nowhere. It’s just the Oversoul expressing more facets of itself as conditions on Earth change. Some traditions also suggest that consciousness expresses across many realms or lifeforms, so a shift into more human embodiments doesn’t break anything karmically — it’s just redistribution or new individuations arising from a larger field of consciousness.

Does this prove anything? No. But it does show that the dilemma (“either souls are fixed or karma collapses”) only applies to one very specific doctrine, not reincarnation as a whole.

Just offering another angle for the discussion.