Anyhow, I asked someone about it, and apparently the Tipat Chalav says that you shouldn’t even put a blanket in the baby’s crib (as WTP said). It seems that the concern is SIDS, c”v, not strangling.
Some people use blankets anyhow (albeit reluctantly) because the baby is cold and needs a blanket, so they consider it necessary.
I suppose that reasoning wouldn’t apply to a Tallis (and even the blanket is controversial).