That premise is completely false from the start. Women don't raise children alone and haven't done so for centuries. Family is the foundation of society. It doesn't cost her more than her partner, who's equally as liable for family expenses as her (usually more).
As I said in the OP, women feel more connected and responsible for their children, and it's more often the men who run away, so it's the woman who carries more risk. So you can either disagree with this observation, or you can blame women for their motherly feelings being in the way of their career.
I'm not against some benefits in exceptionally unlucky cases, for both single mothers or fathers (unlucky != reckless). However systematically subsidising half of the population is a different story.
Humans, if anything, have too much natural drive to procreate until they deplete their available resources. They don't need any incentives, quite to the contrary.
Still, more risk for women in this game.
Men face more risk in other situations. Individual risk needs to be managed by individuals. Compulsory insurance about absolutely any situation as a feature of the State is neither effective nor desirable.
All policies that directly or indirectly reward irresponsibility are to be avoided in principle.