As far as I know, there are only seven states (and DC) that, like Canada and China (the only two of the world's developed nations) have no restrictions on how late a woman may abort her baby. You are correct, however, that more than half will allow abortions with a doctor's consent -and that most of those allow late term abortions for mental health reasons.
As we have discussed on this thread, I believe that Donald Trump's antics have given many Americans the incentive to take a second, and more realistic, look at the question of immigration. Perhaps people would do so on the question of abortion if more of our candidates were willing to talk about it.