You missed one thing: Some women just want to abort regardless, and also have all through history, including prehistory. All those policies you listed there are in place in Germany as the constitutional court ruled that the state has a duty to protect life (also the unborn) and thus has to take steps to minimise the number of abortions, and social means are to be preferred over prison sentences because a) more effective and b) proportionality, but: You don't catch every case with those social means.

Now, if you penalise abortions that fall through those cracks you get backstreet abortions -- which you have no control over. You can't convince people at the last moment, you can't drown them in flyers explaining all the social services they're going to receive and smother them with support. That's why at-will abortion in Germany is decriminalised if you're willing to sit through what's called pregnancy conflict counselling, there's no notes taken or result given in those you get a piece of paper that says that you were there, then there's a three-day cooldown and you can bring the notice to a doctor who now can perform the abortion legally. If you're poor, the state is going to cover the costs (not your health insurance because pregnancy is not an illness).

In a nutshell: For the state to be maximally effective at minimising the number of abortions it has to tolerate abortions being carried out legally, and even pay for them to be performed.

And this, btw, to many an American's surprise, comes from a rather firm "human dignity starts with insemination, the right to live starts with nidation as that's when nature decides to bring a particular life to fruit" type of doctrine. (The human dignity stuff comes into play e.g. during preimplantation diagnostics: You can be tossed out of the pool for carrying a genetic disease, but not for your sex, hair colour, or whatnot).