Late term abortions are already rare, and this type of abortion, in my country at least, is not done because a woman decides she no longer wants to be pregnant, (I doubt this was ever the reason women chose termination), it is done, after a court order is obtained, in cases where there is grave danger to the mother, if she were to carry to term.
In most cases this type of termination is done by inducing a premature birth, as most women want the best option for themselves and the foetus. In many cases the foetus is removed by cesarian section and every effort is made to save the foetus.
Also in many cases of late term abortion, the foetus is already dead, but this is still recorded as a late term abortion.
The emotive sensationalism, falsehoods, and hysteria, promoted by the no-choice crowd, does nothing for their credibility, and shows that they have no rational argument.