They do use "think of the children" as a cudgel to advance restrictions they wish to enact or as a means to scold and attack.
They need women to adhere to their world view, either willingly or forced, and they don't care which. They are more than happy to use force.
That worldview is rooted in male supremacy, and they do mean white, male supremacy - regardless of any non-white or non-male allies.
The world only feels safe to them if everyone behaves as they demand they behave. Otherwise, they become defensive because everyone who disagrees with them is their enemy. They can't let people just live their lives because that might involve a way of life they don't approve of - and that is seen as a challenge to their beliefs and those they simply can't abide.
Anything they see as a challenge to their beliefs is, for them, the same as questioning their very existence.
They need to be able to point to single women who get pregnant as a cautionary tale - the whole "wages of sin" and "bad women" stories they tell other women and young girls to keep them in line.
They need women to die from unsafe abortions for the same reason.
Because those things fit their narrative of how the world should be and how "good girls" should behave.
Being against abortion is not about children. It never was - it's about controlling women.