[1]: https://www.nature.com/news/first-rodent-found-with-a-human-...
It's my impression that after implantation, this process is the same in humans as in other placental mammals. Thus menstruation might be more properly understood to be about flushing unimplanted zygotes rather than aborting unhealthy embryos.
You're underselling this flaw, because it's fatal. A major issue with a lot of pop science is this exactly: the author is much too confident in connecting disparate ideas (because it serves good storytelling and increases trust in the author), when in actuality it's very dangerous to assign intent to things like evolution. For example, a common statement you hear is "evolution caused..." Evolution doesn't have a will or do anything deliberately, nor does it always tend towards the best way to do something or a beneficial mutation. The author also engaged in this flaw by giving fetuses wills (similar to how some writers anthropomorphize animals including primates). So while the doctor goes on in the whole post comparing different species and their different gestational evolution, at the end of the day, it's just a theory that combines different points.
Edit: Downboats? Berry?! Not on my HN!
Sounds like the author tries to address your point.