Normally, the crib is attached next to the bed - with an open side facing the bed so that nursing is more convenient. They still sleep on the firm surface neede

Normally, the crib is attached next to the bed - with an open side facing the bed so that nursing is more convenient. They still sleep on the firm surface needed in a crib (to prevent suffocation, as you noted). That's still a lot closer and more comforting [for them] than having it be in a different room.