Actually what you describe has and does happen.
Personally I can think of two people who I would want around me and my baby in the early days. Neither would be family, they are trusted and close friends who respect me and respect my choices.
They would happily hold my baby if I wanted a shower but they wouldn’t be playing pass the baby downstairs.
If the mum has 1, 2, 3 weeks at home with her baby because that’s what she feels she needs then great. Maybe she’ll need less, who knows.
If she has a supportive partner or a couple of trusted people if needed, brilliant.
You know what happens in lots of families when one person is asked to come and help out?
That’s not fair, she’s picking favourites, she’s shutting us out, we’ll never have a relationship with the baby, my DIL is stealing our grandchild blah blah blah. That is exactly how people behave and you see the exact posts here on Mumsnet all the time.
I agree with you it doesn’t need to be such a drama. I suspect if people were respectful and sensitive then such strict boundaries may not be so needed.