Abortion was never readily available until recent times. Before it was readily available, few women killed their child in the womb. So your theory that outlawing it, would result in more abortions, is DUMB!
And the social welfare state did not exist when abortion was seldom used and yet, people did just fine. So your theory about the need for more social welfare if abortion did not exist, is DUMB!
Again, you show how utterly ignorant you are of history. From the dawn of time, women have taken remedies to "restore menses". In other words, to abort the fetus who was stopping menstration. There is even mention of such potions in Roman times.
The Catholic Church persecuted witches in the Middle Ages because these were the midwives that women consulted for the potions which would induce abortions.
Until women's suffrage became an issue, abortion was a matter between women and their doctors. Many feminists believe that abortion was made illegal to punish women for seeking the vote. And the prohibition didn't last long because women continued to seek out ways to end unwanted pregnancies by legal means (going to countries where abortion was legal) or otherwise (dangerous back alley abortions).
Neither history nor law are on your side. You will NEVER stop women from seeking abortion. If you want to reduce abortions, better start looking at ways of providing better support to poor women who get pregnant. It's the ONLY way to achieve your goal.