Unwanted children happen through marriages as well.
Plenty of abortion clinics running in Pakistan profitability (Im focusing on Pakistan as this is topic that pertains to it).
The issue here is family values and not sex. Family values control sex outside of marriage, not laws. An unmarried man in his mid 30s who is unable to woo a woman will eventually be temped to visit working women no matter what his beliefs are.
A young teenage couple will engage in sexual activity because family values did not enforce the prohibition of the activity enough and society did not offer them a way to recognize their nikah.
After all, the word nikah means to pierce a veil.. the rest of it is a social contract which then is publicized to give protection to both parties in case either of them breaks the terms of the contract.
It is not laws alone that enforce sexual responsibility but family values. When you have already lost Family values, then all the laws in the world will not stop a physical union.