We just called them "Blanket Sleepers", and my kids did sleep in them when they were babies, but I always put a blanket over them even with those on.
We were brought up very different than the "modern" ideas and dire warnings of injuries, and somehow we all survived, and so did our children. We didn't have 1/3 of the "safety" equipment that is used now, and we all survived it. I think all the over-cautiousness has only driven consumer product sales!! Sure, take reasonable precautions, but I think a lot of this is way over-hyped!!
Now "the experts" are saying that babies aren't learning to crawl because they aren't being put on their stomachs after all the super-hype about SIDS. We would put our kids on the floor on blankets on their stomachs with toys out of their reach so that they would scoot and try to get them. That's how they learned to move. We had to physically get down on the floor with my little grandaughter and work her arms and legs to teach her to crawl because my daughter wouldn't put her on her stomach!!