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 think it depends on the gynae himself/herself whether he/she is pro-natural instead of relying on the hospital's c-section statistics. Normally a gynae has protocols on whether to proceed to c-section, e.g. when baby is in distressed or high risk pregnancy. Under normal situation, most of the gynaes will let you try natural birth. You might want to search online and read up reviews on your choice of gynae, whether he/she is pro-natural birth.