It must be either a cultural or familial tradition thing.
We were "around" for the birth of both of our grandkids. In one case, at my wife's hospital here in Parker. In the other, we were visiting the kids that live in WA over the holidays and around the due date with the hope we would be in town when he came.
In both cases, we asked them what they wanted. Answer, "Privacy."
Great, let us know if/when you need us or are ready for visitors.
I realize there's two sides to this, often very polar, but I certainly supported their decision and frankly had no reason to go hang out at the hospital in either case. We were minutes away from one, and less than an hour from the other when the time came. One of the other grandmas packed her own bag and was bound and determined to spend the night at the hospital with my son and DIL Only after repeated and stern demands by DIL for her to stay home, did she agree to keep her distance until they were ready to take visitors.
On the other hand, there were friend's of the kids telling them on FB they needed a week or more of alone time, even without the grandparents getting to visit the newborn. Granted, the kiddo isn't going to know what's what from one or two brief encounters, but it's a proud and emotional experience grandparents cherish. I don't believe they realized we were in town, and staying with the kids... We limited our time, and gave them their space. Of course, we also knew we would still be there for a few days after they were discharged.My wife's real goal was to be there to help and support DIL and baby at home for the first few days and that was achieved.
My wife is a L&D nurse so babies in general are pretty run of the mil for her, though she is the proudest grandma I know. For what it's worth, in 1984, my pregnant wife was staying with my parents the last few weeks I was finishing an AIT and clearing post for my permanent duty station. I was on the road traveling back to my hometown, wife, son, and family, and the expected birth of my second. I arrived in town and called the house, only to find out I had missed the big event. On the upside, my mother acted as my proxy in the delivery room and was thrilled with the privilege. I was disappointed that I wasn't there, but that's life.