Earlier quoted context omitted.
There are other reasons people want to get abortions, such as knowing they can't provide for the child or give them a safe/stable household. Adoption is rare, and the foster system in most countries absolutely ruins kids. So those aren't good alternatives.
I'd hope someone would know fairly early in the pregnancy if they will be able to provide for a child or not. (i.e. before the baby can feel pain, is basically a complete human being, etc.) That's why there's so much interest in defining limits around abortions. Late term abortions are pretty much described as horrific by the vast majority. There should be room for political agreement here.
To be clear, you are right that a late term abortion is pretty horrific. They're also -traumatic-. No one is -intentionally- waiting around to get an abortion; there isn't room for political argument here because anyone who finds themselves pregnant at a late stage and doesn't want to be is already in the case of "reasonable exception". A medical complication, a change in financial status to where she can't support it (when before she thought she could), etc.
No one is finding out they're pregnant in the first trimester, and then just can't make up their mind until the third, and we as a society need to set a date she has to make up her mind, or force her to keep it against her will. That's a made up justification, and as we continue to see, the same forces that make that justification don't even stop there.