If you knew your shortlisted Private & reputed maternity hospital has high cesarean birth rates vs a decent Government hospital, would you change your mind?

I agree with @diana, I would focus on the gynae rather than the hospital. I am sure you must have done your research before choosing a particular gynae. Over the course of pregnancy, both of you must develop complete trust in your gynae to make appropriate decisions. If not, then I would recommend changing. Hope it helps!!