I just delivered at a private hospital; I'm a FTM and have the same hopes as you but had to do an e-csect so let me share my story. On delivery day, it took hours for me to get 4cm dilated (need to get to 10cm), and the doctor highlighted that there were instances when the baby's heart rate dipped during my contractions. So there's a chance it may drop more during actual labour and if the baby gets stressed will have to have interventions or a more complicated c-sect so I have to decide whether to push on for natural birth or not. When I asked for his advice, it's to c-sect due to the possible risks, and also I'm dilating really slowly (I'd been in hospital for 9h now) so it'll remove the waiting stress (not his exact words). I was not pressurized, but he laid out the facts and it is impossible for anyone to know if the risk is just 5% or 80%.
I chose my gynae based on stellar Google reviews and a reviewer mentioned he is sincere and pro natural birth, but taking a second look now I see almost every reviewer had a c-sect and were thankful for his skill. My point is that at the end of the day the decision is up to you, not the gynae. He may be advising me to do c-sect coz he wants to just get it over with, or he may just be highlighting it for full disclosure and the risk was actually really slight, or it was actually quite a big risk and I made the right choice and saved the baby, but I will never know. So I'll pay more to choose a gynae for his expertise in case of complications, but unless you already have a gynae in mind and are willing to pay more to see him I don't see a value in paying more to avoid a gynae who is pro c-sect on delivery day. I hope this helps.
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