Most species with horns and wings do not give birth to young with those features already developed enough to be "proper" for exactly this reason. Birthing hips are considered a desirable feature because they make multiple goes at producing viable progeny more likely, but evolution historically steers toward having anything that would have trouble fitting through the door get built up afterward.
Well, the birthing hips is almost solely a human thing with us being one of the few entirely bipedal species, which introduces unique dilemmas both for our birth canal (keeping the thing inside during the whole pregnancy) and pelvic inlet (narrow hips better for moving, wider for birthing). Like, even Kiwis with their eggs (just web search it and be amazed + horrified) have a safer and less taxing birthing process than us. So consideration for horns and such isn't all that birthing hip related.
This bag of nitpicks aside, you're 100% right. Even hedgehogs have soft spines when born.