You are right, that it is best to wait to clamp/cut the cord until the blood stops pulsing. It usually only takes a minute or two. With my first, she wasn't breathing, and they had to cut it right away to whisk her off. I did try to stop them to remind them I wanted to wait, but they said it was necessary to cut it immediately. They absolutely have to get those babies into the heat and suction them immediately. There would be no benefit to waiting for them.
My second, They agreed to wait to cut the cord, but they always forget all special requests and you have to remind them.
I also had them wait to put in the eye ointment because the babies are most alert right after delivery. They can't see through the ointment. I preferred to have my baby see me during our first binding moments. I did this with both kids, and they put the ointment in as soon as they fell asleep. Again, you have to remind them, but it is well worth it. Plus, you get those first pictures without the goopy eye stuff.
As for the placenta delivery, I didn't have any problem with either kid. Pulling can be dangerous, and shouldn,t be done unless you are refusing to push it out. I was surprised that it really took a strong push, but there was no pain or complications. It is essential for them to push and massage your uterus in the 24 hours following delivery, but that is something different. My aunt was my nurse and told me a little secret. If you tighten your tummy muscles every 10-15 minutes or so, you can shrink your uterus on your own without all the painful massages from the nurses. If your uterus is shrinking faster than required (from your exercises), they will just check you and leave you be.