In my experience, people with perspectives like yours tend to drastically overestimate how many abortions happen later in pregnancy. Nine out of ten happen before 12 weeks. And of those that do happen afterwards, the vast majority are due to the discovery of medical risks to the mother or fetus. Very very few people are just casually waking up and deciding that an abortion sounds like a fun way to spend the afternoon. I'd also remind you that a good 20% or so of pregnancies end in miscarriage. The Right likes to spin up this twisted fantasy of women and doctors going on baby killing sprees for fun and profit, and it's simply not the case. "Post-birth abortion" is not a thing to any remotely significant degree. As I understand, there are some exceptionally rare cases where, upon birth, it's discovered that the baby has an immediate severe health disaster that will result in it having perhaps a few days of miserable suffering before dying, and in those situations, it's instead euthanized in what is naturally a life-defining trauma to the mother. To take one of the most tragic experiences a hopeful parent can possibly imagine and pervert it into a shallow political talking point is something that I will not dignify with any additional response.
It sounds like you do acknowledge that there's a lot of nuance and complication here, and that there are legitimate reasons for abortion. Given that, I don't see why there's a compelling reason for the use of government power (amusingly, from people who claim to be for small and limited government) to interfere in complicated medical decisions between parents and their doctors.