There are two sides to this discussion regarding the welfare of the child in question.
The first is the risk argument - what is the chance that something could happen and what would be the consequences? A valid philosophical argument that we all put aside in favour of social convention (the travelling in a car example).
The bringing up of a child, in most of the societies we all come from, is more than keeping that offspring alive until it can fend for itself. It is being responsible for the physical, social, spiritual, mental and emotional welfare of that child, in as far as it is age appropriate to be, given the needs of the child to learn to support itself.
I think that despite the deprivations that go with it, once we become parents we should shoulder the responsibility of that role. I don't like not being able to go out because I have a child whose greater needs are to be at home with suitable supervision. However, if I were a child left with no protector in place, I would not like to feel alone, or fearful, or distressed, or uncomfortable, and without knowing why nobody came or whether the situation would ever be better.
Having said that, I'm not a great believer in disturbing a sleeping baby. I personally have never felt the need to constantly check on my children when they are sleeping. I have always responded quickly to unusual noises or sounds of distress from them and I don't think that leaving a child where there is no realistic chance of responding suitably in a baby friendly timeframe is one which fits with my view of good parenting.
Thank you OP for being the person who watches over this little family. I'm sure with your knowledge and good sense both the mother and child will get the support that is needed. There is nothing wrong with your instinct.