I slept with my kid (I'm a father) for almost a year and trust me, you're still deeply aware of them when they're next to you.
Smothering does happen, statistically speaking, but the odds are so tiny and the benefits so great, it's basically a misinformation campaign based on bunk 1950's science.
When I read more into the numbers it seemed that where co-sleeping has a real risk is when it happens outside of the bed, when the caretaker falls asleep in a chair. All of the deaths get lumped together and we are just told that you need to X so you reduce the risk of SIDs. It kinda sucks because it is so hard being a new parent, it would be nice to better understand up front what the real risks are.