Yes - PPH can happen to any woman after any type of delivery.
Yes - an injection post birth to force uterine contractions can stop bleeding and saves lives.
BUT the number of women who will have an immediate and catastrophic PPH, after a spontaneous unmedicalised birth, where delaying a syntocinon/synotmetrine injection by any time at all after the birth has tragic consequences are very very few. For the vast majority of women who have had a straightforward birth a managed 3rd stage is not immediately necessary, and the decision to move to a managed 3rd stage can be made as and when it appears prudent to do so.
If you want a fully managed 3rd stage - that's fine, its your choice. If you need the drugs due to having a PPH - aren't we lucky to live in a country where they'll be readily available? If you want to take a "wait and see" approach - that's also fine and also your choice and I think there is a lot of information to support the position that this is not a foolhardy or irresponsible decision.
Re. retained placenta - there may be no conclusive evidence, but there does seem to be a general belief that it is more likely to occur after the jab as the ergometrine component forces the cervix to close, limiting the time available for the placenta to detach and be expelled (in my mind it's something like 15 minutes, but PFF may be closer with 7 - either way, not terribly long). With a physiological 3rd stage that time pressure is not there so as long as mum and baby are OK and happy enough, it doesn't matter if it takes 1/2 hour, or an hour - or even longer.
SurprisEs - MWs (or Drs) are meant to receive your informed consent before doing anything to you. So if you were given the jab the MW should have explained what it was and why they wanted to do it, and should have waited for you to agree that you were happy before proceeding. Some HCPs do this better than others...