To be entirely fair I think what you say is technically and clinically correct if the midwifery carenin labour is optimally tip top.
When DS1 was born at 36.3, spontaneous labour, the midwife blamed a dropping heartbeat on a faulty belt - twice. The third time, DH opened the delivery room door and blasted "I want a doctor in here and right now". Cue a senior midwife appearing and the emergency button being hit, heralding the appearance of about a dozen people.
DS1 was posterior and had the cord wrapped around his neck. He was too far out to be pushed back for what should have been an emergency caesarean. I was hoisted onto a birthing stool, and given one more push as the Dr got the forceps ready. The midwife cut the cord whilst ds was still inside. I don't know how I did it but I got him out with that one push rupturing a blood vessel in my eye and suffering a prolapsed bladder and some sphincter damage (neither of which the NHS gave a toss about so thank goodness for health insurance).
The baby was very "blue", took minutes to resuscitate and had an apgar score of 6 after 5 minutes. He had to spend the night in SCBU. Fortunately all was well.
Do forgive me but I think a caesarean would have been better and safer than what happened to me and that was in the halcyon days of 1994.
When pg with dd (after a tragic, expected and well managed loss at 27 weeks) she was breech and big and turned two days before a planned section at 38 weeks. I felt I could not justify surgery that was not necessary but with the promise that the baby would be delivered by a very experienced midwife - unconditionally. The obstetrician agreed and the Head of midwives came in for the birth. At 41.5 weeks I had had enough and was induced. I had the pessary and refused to have my waters broken. After 8-10 hours they wanted to put up the synticynon drip which I agreed to providing I had an epidural first. My waters broke waiting for the anaesthetist and labour was well underway by the time the epidural wasnin. The drip was never started. DD arrived swiftly and calmly. It was a very cathartic birth.
My care with dd was obstetrician led and I saw only a consultant throughout the pregnancy. Mutually respectful conversations took place and there was no nonsense chatted.
My advice @horchatatresleches do not be advised by a midwife, please request to discuss any decision making with an obstetrician. Secondly, if you are induced you can insist on an epidural before they put up the drip.