It's always made perfect sense as the biological norm to me. Along with the oxygen support until breathing is established, the benefits of blood supply evening out both sides of the navel were pretty compelling to me. Having read up extensively about this before the birth of my 3 oldest, I requested it for their births in 1993, 1995, and 1997.
In the event DS's labour was augmented (which is a contraindication as it can force too much blood into the baby apparently). He was rather badly jaundiced. DDs 1 & 2 were home births with delayed cutting. Absolutely fine. DD3 was born as a crash CS so not sure what happened but she did get slightly jaundiced. I had been on syntocinon and she was pretty ill so fairly unlikely they delayed clamping. I really must get around to going for a debrief some time.
A friend had a hb and delayed cord clamping with an independent very laid-back midwife. Even her midwife was getting pretty worried and getting ready to take my friend to hospital when the placenta hadn't appeared after 7 hours (everything else was fine) and the cord still had a pulse. As my friend stood up to walk to the ambulance, the placenta plopped out.