'The USA' does not have stringent abortion laws. Some states do. Some states have retained the right. In some states the discussion on restricting abortion will never happen. Abortion access is a state remit.
I live in a state that has not changed abortion access, where politicians' electoral campaigns include a pro choice platform. My state is surrounded by states that restrict abortion access and there has been a huge uptick in travel for abortion services since the SC decision and subsequent legislation in neighboring states.
There are also baby boxes here. This is because it's far better to place the baby in a safe, warm spot than out in a dumpster or on some cold doorstep. Before the legislation was passed that resulted in the baby boxes, there were many tragic deaths if babies born alove and healthy, every year.
Baby boxes are located at the five fire stations, at the police station, and at both hospital emergency rooms in the town where I live. There are no questions asked at the time of drop off apart from perhaps a question about medical attention needed for the mother. It is understood that the attraction of a baby box is the anonymity and the ability to walk away with no judgement attached plus the benefit of knowing your baby will not die of cold or starvation, or be bitten by ants or other critters in some dirty alley. But there is cctv, and strenuous efforts are made to find the mothers and provide support, both medical and emotional. Iirc, a mother has 30 days to reclaim the baby if she changes her mind.
Women don't always see abortion as a viable alternative to an unwanted pregnancy. Women don't always see social services as potentially supportive allies, or they feel they have a situation in hand and don't want interference. Some are in denial about their pregnancy until it becomes impossible to disbelieve. There is usually a lot wrong in the life of a woman who places her baby in a safe haven box; a hidden or unwanted pregnancy and a baby to deal with are only the most visible part, the tip of the iceberg.
Babies can be left in a box up to 30 days of age in my state, though nobody is going to argue that a woman went over that time limit. It's not always a matter of raging post natal hormones, panic, or confusion, that cause the decision. There can be PND, or an abusive relationship, destitution, relapse into drug use having given up during pregnancy - any number of different reasons behind the decision really, in the 30 day time frame. Yes, some states have much shorter time frames, and post natal mental issues can play a part, but usually a woman has planned enough in advance to locate the baby box and find some way to get there within 72 hours to a week of giving birth.