I actually find abortion with no exception for rape to be far more ideologically pure position than abortion with exceptions for rape.
The one that makes the least sense is restriction on abortion even in the case the fetus cannot survive. That one is far less defensible than not having a rape abortion exception as it can't be explained from the viewpoint of the rights of the mother nor from one of the rights of the fetus.
It's defensible when you realize that forced pregnancy is viewed by many religious people as a punishment. "If you didn't want a baby, don't have sex" is very commonly heard in private conversations with religious people.
Because pregnancy is a holy punishment, the consequences, even death, are seen as moral.
This is also why the rape exception is more common than the medical exception. A mother dying because of an ectopic pregnancy or because she was too young to have a baby is god's will.
I initially held your viewpoint but after engaging a lot of people I realized they often had pretty similar views on life and liberty as mine, they just were looking at it from the viewpoint of the fetus rather than the mother. From that perspective it just doesn't make sense at all to make an exception for rape.
People will almost never take the "it's a punishment" position in a debate because that's not a popular position to hold and it's pretty weak morally at the end of the day. That's why the "life of the fetus" approach is most frequently taken even though it leads to absurd positions. For example, pro-life people will very often be put into a difficult position when the notion of IVF comes up.
That's what betrays their true views, IMO.
I've simply had a lot of private conversations with people on religion (I was mormon for a long time and served a mormon mission). That's where my opinion on the actual underlying anti-abortion attitude comes from. It's lots of private conversations in safe spaces. The fetus life, frankly, is almost never brought up as a reason.
And, as I pointed out, it pretty well explains why anti-abortion laws have weird boundaries if they were purely about the life of the fetus.
Most nations still have social support and government responsibility as last resort, which equally can do the job of supporting children without willing parents, but then people return to the punishment/moral angle that if men don't want to pay for children then they should not have sex.
Look to how quickly people reaches for the morality position and we see how little friction anti-abortion policies has to overcome.
What I expect to see for those that view it as primarily punishment is little outside of child support for kids. Penalizing the "dead beat dad" as it were. I expect those governments to not provide child support, tax breaks for parents, or any sort of welfare/support/minimum standard of living for parents. That is to say, the answer to "how hard would it be to be a single parent" in those government would be "very hard".
For governments that are solely looking out for the welfare of the kid, I expect to see a large amount of support for kids, especially for poor families. I expect some help with childcare, housing, etc to make sure the kids are well cared for.
The closer people holds to those values, the easier society accept laws like anti-abortion. Religion do play a supporting role in this by holding onto the values, but is itself not always in the center.