In a preindustrial society, your children are your social safety net. Having a bunch of kids insures that there is someone who can be with you as you age. Also, some of those children are likely to die, so if you want to be taken care of, better have an extra child or three. And since you are likely farming the land anyway, it's fine to have another pair of hands to do that around, means more work gets done and so more food and actually more wealth as well, once that kid can help out. And if you are not farming, congrats, you are one of the few people in preindustrial society that are rich and you don't have to worry at all about feeding and housing your children.

In a modern society, there is supposedly social safety nets that make having many children less necessary as a survival tool. Now these are being eroded and living conditions get worse, but people aren't simply going to forget they are supposed to be there. It is known how rich you have to be now to afford children, because every child is a real burden on your wealth, because the kid will not be able to do any useful work and will need costly help in the form of education to be ready to even leave the house in 20+ years. And it is bad parenting to not provide for your child. Most people can do the math if they can afford that cost on a napkin and for many, the answer is no. And yea, of course you could just not provide your child with what it needs, but that's not exactly a recipe for getting the child to help you out later.

So no, getting even poorer is not going to raise the birth rate. Maybe in the long term if capitalism collapses and gives way to feudalism 2, electric boogaloo, where a few trillionaires own everything and everyone else doesn't kill them and instead works for them for some weird reason.