The justification given for paritial birth abortion ban was some horrific accounts of very late term abortion in which breathing babies were born - limbs cut off attempting abortion by a doctor - who then smoother or other terminate the life of the now born baby. That is unthinkably horrific and simply too savage to accept. I do think society can set a deadline around when a woman can abort upon independent-life viability to prevent such nightmare scenes ever happening again.
So my answer is absolutely and regardless of why. In some situations it might be immoral, but not my moral decision to enforce.
An example might be a woman who becomes pregnant deliberately with a man - both wanting a child - and then as a pissy mood revenge against the bio-father aborted to declare to him hurtfully "I killed you son, how do you like that you asshole?!" Very immoral conduct. Not illegal though. There are powers and inabilities both genders have in parentage as simple reality.
Exceptions? I think society may prohibit abortion if it wishes too, but only when the host mother's body is no longer a necessity for life - again acknowledging there are complicated gray areas. For example, should a woman be allowed a C-section abortion in the 6th month, resulting in a severe living premie? I could accept a "no" to that. I'd have to think more about those type issues as they are quite different.