EDIT: Let’s cool it with the downvotes, dudes. We’re not out to cut funding to your black hole detection chamber or revoke the degrees of chiropractors just because a couple of us don’t believe in it, okay? Chill out, participate with the prompt and continue with having a nice day. I’m sure almost everybody has something to add.
In the UK, it’s not an absolute no, but a “be careful”. Interestingly, my wife’s sleep habits changed considerably. She was instinctively aware of where our baby was, even while asleep.
The main dangers seem to be either the dad (my instincts were far less affected) or a sedated mum. It also becomes a lot less risky when the baby can move. Our daughter was perfectly capable of making her comfort concerns felt.
It’s not zero risk, but it’s far lower than you might think. New mother sleep deprivation is quite different to normal sleep deprivation. I see why the default advice is what it is, however.