It's interesting to me that the states continue to push this point, since SCOTUS has so often attempted to assert that almost no restrictions are acceptable. Nevertheless, I suppose every time you pass a law, someone has to go to the trouble of challenging it in court; perhaps over time they expect to convince the federal courts that an unrestricted access to abortion is not acceptable to the people of many states within the United States.
Also, some of these "restrictions" are just restrictions on who has to pay for abortions. Given the deep moral issues involved, it is surely reasonable to say that no one should be forced to contribute to abortion against their will. That means no taxpayer funding, and it also means that conscience exceptions ought to be thought reasonable. We often hear from the pro-choice party that a woman's right to make a decision on the morality of abortion for herself ought to be respected; but surely we ought also to respect the moral choices of others who are horrified by the practice, and not force them to enable, participate in, or fund what they regard as a killing of an innocent.
Of course, it's also problematic to suggest that a woman's right to choose should be unilateral; it runs up against the common sense notion that it is not wise to allow someone to be the judge in their own case. It is not that people mean to be unfair, or even think that they are judging unfairly; it is just that we all have unconscious tendencies to over-emphasize our interests when we are judging in our own cases. This is a well-known fact of human nature that applies to all people at all times; naturally it applies here as well.
Thus, even though I am sure that most women who go through this decision believe they are carefully judging the matter, it should neither be surprising nor controversial to suggest that these sub-conscious processes lead them to judge their own interests above those of the father or those of the child. The father may or may not want the child, but the child's interest will surely often be best served by being born even if it is then given up for adoption. Sadly, we find that all these new restrictions occur in a context in which too often abortion numbers remain at near record highs, and adoption referrals decline.