Yeah, you're not looking in the right places. The nuance is covered in every first world country. The truth of the matter is that the vast majority of abortions take place in the first trimester. "Later" abortions are often because people either lack the resources to take off work and travel to where the abortions are offered, or they're fetuses with deformities incompatible with life.
It's easy to talk about the day after pill, but if you're a woman with an IUD or on the pill or using condoms, you're not taking a day after pill as well, and the fact is birth control fails. There is also a huge amount of coerced sex that happens, and when men are horny, birth control is the last thing on your minds. A girl who is 12, 13, 14, 15 and coerced into sex may not have the presence of mind or the transportation or finances to get the day after pill.
Curbing abortion numbers means education, affordable healthcare, easily accessible birth control and better treatment of women and girls, all things conservatives are loath to go along with. They prefer the shame and punishment of forced pregnancy and childbirth.