The reason for this is that we tend to sleep deeper now than our ancestors. Because of this, we are more prone to roll onto a baby, and not wake up.
It can still be done, you just have to avoid things like alcohol, that stop you waking. You also need to make sure your sleeping position is safe. Explaining this to exhausted parents is unreliable, however. Hence the advice Americans seem to be given.
Fyi, if people want a halfway point, you can get cosleeping cribs. They attach to the side of the bed. Your baby can be close to you, while also eliminating the risk of suffocating them.