The lack of interest in this baby isn't a surprise as it is the spare. George is the future King and this child, although it will be much loved within the family, is simply the extra - the spare - and so the interest in much lower from the press and the public. They may not even announce where the baby will be planned to be born. There have been reports of plans in place for a transfer to Cambridge in the case of an emergency and the nearest hospital is in King's Lynn (if she is at Anmer when she goes into labour.)
I doubt that the world's press will line up in front of any hospital. This child is simply the 'spare' and therefore will become less important over time - like Harry is less important to the family now since the birth of George and with this impending birth he becomes even more irrelevant. There wasn't as much interest in Harry's birth as there was in William's because the future King was here so the spare was just that.
