You don’t need to be rich, and it doesn’t matter if it’s public or private. Having lived in 6 countries in Asia over 20 years it’s never been expensive, difficult, dirty, or anything like you describe.

Well the exception being Singapore. That was expensive but covered by insurance so it still cost $0.

Edit: another thing. What is with the west more or less forcing natural birth and kicking you out of the hospital the next day? I would have to give birth in a western country. Thankfully my kids were born in Asia. Hospital took care of baby and mum for 6 days then we left the hospital. Cost was 2 weeks salary.