The subsidies have an ontological value in that they improve the quality of life for the child. So removing subsidies will actively perpetuate and increase the very systemic issues that many antinatalists care about in the first place. You address this too, I'm just expressing agreement that simply removing chiodcare subsidies is not ethically simple even for staunch antinatalists.

In general governments ought to be working to support the people they represent. To me it seems an antinatalist who's goal is to reduce suffering would want to introduce things like a basic income or some such to improve the quality of life of those who do exist, not further take from those who have yet to be.