I think it is sad when people are forced to make decisions they don't want to - whether that's working or SAHM. That said, I also don't think the govt should be subsidising people not to work. If you can afford to make that choice, then great - but I don't think people should expects others to pay for it (through their taxes). Working should be the default position IMHO.
I also think your OP is full of assumptions... Many people do choose to stay in work to maintain a lifestyle. I know friends who have moved and downsized to enable the mother to stay at home, others where they have remained in very small houses etc. I know if I moved to a much smaller house, on a main road in a cheaper town, I could knock 60k off my mortgage. This would enable us to have one SAHP. But it's not a choice we want to make. for many others, I think they need to work to maintain a lifestyle, but sometimes there are alternatives for those that don't!
Also, Why do you assume that of the people who work are going to automatically be putting their babies into institutions? Amongst my friends, grandparents have been a very common source of childcare, as have mums working evenings / weekends do childcare is not needed. Then there are childminders... I know more people who have gone down this route than have put their children into full time nursery. In fact, out of my friends only 1 returned to work full time. All the others went part time or gave up completely.
Part time working seems to be a very common option (with most of my friends working 2 or 3 days) - this is not exactly the farming out of children you picture in your OP.
I guess what I'm saying is that amongst the people I know, the choices they have made have been very different to the scenario you paint. The majority of coupled I know have made sacrifices to enable the women to work part time (I do know very few women who do no work at all - it seems to vary between part time career work, a few hours shop work or even just looking after someone's children for a few hours a week). This seems to be the situation amongst the overwhelming majority of people I know - not the scenario you paint.
Sorry it's long!