Or maybe societies could instead make the prospect of having children less onerous? It's not an uncommon story in America that a couple will choose to stay unmarried when having children so that the mother can qualify for benefits like childcare (which, if you haven't had children yourself, is staggeringly expensive when it's available at all).

To think that the solution here is to penalize women even more is insane.

This is the extremely marketable "solution". Easy to sell to voters. The problem is that it does not work whatsoever. There is no evidence anywhere that transfers to mothers increase birth rates, or that transfers to women increase pairing rates (the upstream problem of birth rates).