I don't see waiting a week as a big deal, if the couple wants to do that. This is one of those situations where YMMV depending on a whole slew of factors, none of which would be the same for any couple. Things like: Difficult birth? Toxic relatives? Distance? Siblings or childcare needed? Did they even WANT help? It all plays into it.
My MIL was a toxic person with no boundaries whatsoever, and if I had produced kids, she would not have been notified until we were home and ready to receive visitors. So definitely not for at least a couple of days, and I would not have wanted any visitors in hospital. Friends of ours had a baby via a very traumatic C-section, and weren't sure he would survive for a couple of days. Until he was out of danger, the only people notified were their parents. No siblings, not even dear friends. Another couple waited 3 days after a routine birth just so they could get settled. Again, their call. Being hurt strikes me as being a bit SS-ish, but then I'm not a baby person either...I didn't see my latest nephew until he was 6 weeks old due to work travel commitments!
When my first nephew was born, their ILs visited no less than 12 times in 2 days, and stayed for at least an hour each time. It was way, way too much, but being as it was their first child, my S and BIL hadn't figured out that they could say no. Next kid, no visitors allowed until they were home, and everyone was much happier.