I'm not aware of any stigma from women being stay at home moms. My impression is that most, if not all, people are aware that money gives you power (or freedom, if you will). And who doesn't like freedom.
There's also less security of income for everyone, so a household relying on one spouse's income is risky. Especially if there's no extended family around that can come to the rescue in the event of loss of income.
>Why do we assume having a career requires more ambition than wanting to raise a healthy family?
Because it's too easy to say "I want to raise a healthy family", therefore it's a poor signal. Proving yourself with work, well remunerated or not, is a better signal. So I would say there are a lot of incentives for women to work, but not because society stigmatizes it, but because it leads to optimal results for women (and men).