The cost of daycare and education is so immensely larger than the cost of a car, that I don't think cost of a car is a factor. The important consideration with having a child, or another, is how could you possibly afford the daycare and later school.
The car seat related drop predates high daycare costs. In some places, high daycare costs aren't the primary concern: it's infant daycare waiting lists longer than 9 months.
Grandparents used to look after young children. Maybe we should incentivize that structure again? I'm open to other ideas.
Right now, childcare can't be affordable without the workers being paid exploitative low amounts. We should fix that, that's exactly the sort of problem that having a society is for.