I had considered doing a natural third stage but my OB recommended against it. He said there is a higher chance of haemorrhaging if you opt for a physiological approach and he has witnessed it on several occassions. That was enough for me to think twice about it.
My mum is a midwife and she is pretty easy going.

Her take is she has been practicing for around 40 years and seen the trend swing between both managed and physiological third stage.

Her personal opinion (which I absolutely trust and will practice myself) is that she has seen an increase in PPH with a physiological third stage vs managed.

It is a very personal preference, but she explained that the injection allows your uterus to contract efficiently after the birth and essentially cauterize off any small bleeds AND ensures the contractions birth the entire placenta - not just parts.

So based on her observations in the field, I trust medicine in this issue.

I think there's a fine balance between a wholly natural approach and making good decisions that can still make it a natural experience IYKWIM?