Logistics on legality?

It is very easy to have abortion morally illicit. But where I have issues would be how to implement abortions only for rape and incest. There seems to be no economic reason to have any restrictions on abortion. Economically if more people have abortions then less people will be on welfare. Also how would government keep people for having abortions without a huge breach on privacy?

I am looking for a solid argument on every aspect against my pro-choice friends. So far they only have that its the mother's choice (apparently something with human DNA isn't a person) and that the logistics side (which does make sense).

Edit: http://gifsoup.com/download.php?id=2246960&d=animatedgifs2&n=i-m-so-confused&s=o