DD had a moses next to my bed. When she woke, i used to sit up and feed her, crying with exhaustion, worried if i feel asleep with her next to me lying down, something would happen! It was like torture some nights as she fed every 1.5 to 2h when newborn, as she was prem, she had a fair bit of catching up!
As she got bigger, I worried less, and she was able to control her head from very very young, in fact, I genuinely don't remember her not having some head control... anyway, she slept o her back and turned her head mostly, to feed, I'd move her on her side, and she'd roll back to her back... she was fine, and I felt more relaxed about it then. So we went to feeding pretty much all night, on and off, in bed with me. Meant I got a heck of alot more sleep. though it'd really annoy me sometimes! I'd have to take her off... until she learnt how to lift up my top! Then I had to wear a bra to stop her helping her self, as I'd get sore from SO much sucking... then she learnt how to undo the drop down cup on it...
It saved my sanity TBH. Now she is 15 months, she gets into bed with me at 5-6am, by either me, or DH, and she just suckles until we are ready to get up! Its great! She sometimes goes back to sleep, sometimes not. She just goes from one side to the other, climbing over to chage side, or lying on my body,, or standing up with her legs straight and body bent, like a baby goat or something... She wont wait longer than about half 8 though... thats when the hair pulling, pinching and last resort biting starts to wake us up!
I think also, that if you follow all the other guidelines, like bedding, pillows etc then it surely can't be any worse than them on their backs. I assume its due to the fear that hey would roll onto their front, if on side?
We use a bed safety rail on my side. She used to have her own sleeping bag too, and ours went no-where near. I also made sure our pillows were not near her either. Though now, she climbs onto them, under our duvet, and sleeps o her tummy!