Public then switch to private for less cost overall?

Hi all! First time mama here, I still have not seen a doctor but have already tested positive with at home test kit. I heard that it’s possible to start with a public hospital to get everything subsidised, but when closer to delivery date, switch to private so I can experience the comfort/overall better experience at a private hospital. This is just for less cost esp with the check ups in 1st and 2nd trimester. Has anyone had experience with this?