Nine to twelve weeks is a long time, if you're in serious psychological distress.
I do think induced labour should be offered, as I've said, but I've gone over the reasons I think killing the foetus may be preferable – starting with, if it's alive, then the woman is still a mother. The child now exists, which, if it's a product of rape or incest in particular, could be very psychologically damaging.
If the baby is a product of an abusive relationship and she keeps it, it ties her to the father permanently. But regardless of that, she either has to raise a child she didn't want, who may be a constant reminder of trauma, or relinquish it, which would mean she now has a child out the world who may seek her out when they're older.
I also suspect many women wouldn't relinquish the child once born, and if they're seeking late term abortion because their lives are chaotic, they have drug addictions, are vulnerable, are in an abusive relationship, or other similar reasons, it may not be for the best.