I love my private OBGYN, and private Obstetric Hospitals are lovely, but I do agree with you that LSCS should not be based on the indication of "convenience", but rather on obstetric necessity (for me, that would be obstructed labour, foetal distress, breech presentation, placenta praevia, etc).
The problem the private sector faces is that private OBGYNs are on-call 24/7 every day of their life, which even for the most dedicated, is rarely sustainable for them personally. I think the only solution is for private OBGYNs to cover each other on certain weekends and holidays, so they do get a break. Hopefully this would help reduce elective LSCS rates. And as private patients, we need to be reasonable and accept the fact that the OBGYN who has provided our antenatal care, may not be the one delivering us. My OBGYN hasn't had a holiday for years, which cannot be good for her...and may result in burn-out, which would be such a shame. I think it is a real dilemma for private Obstetrics.