You don't seem to understand the reasons why most women have late term abortions.
Here are the reasons cited for late term abortions... they don't fit with your logic and perhaps knowing the reasons may cause you to change your opinion some (The Guttmacher Institute was founded by planned parenthood).
"The Guttmacher Institute also surveyed a large number of women obtaining late abortions and asked them their reasons for doing so. It found:
Only about one percent of second- and third-trimester abortions are performed for fetal anomalies, or eugenics
One-third (31%) of the women surveyed said that they misjudged how far along they were
One-fourth (27%) said that they found it hard to arrange an earlier abortion
14% said that they were afraid to tell their parents or their “partner”
The rest gave reasons such as taking their time to decide or waiting for a change in their relationship."
You might find these reasons viable but the vast majority of women including pro choice women do not. It is fair to say late term abortions are not very common, but it is wrong to say, the reasons are medical necessity.
This and similar research is why people want to be very specific when it comes to late term abortions when a healthy viable baby is involved.
Other studies point to the following...
Science has driven down the viability date to 20 weeks for a healthy developing baby. So, the "back half" of the second trimester often involves "viabile healthy babies". And as such well over 70% of Americans including women oppose abortions for this group, including the majority of people living in progressive states. Many states will adopt a revised Roe v Wade standard based on new technology.
Prior to viability but after 13 weeks, the percentage of people that oppose elective abortions drops to just over 50%. I expect many "purple" states to establish the first trimester as the cut-off.
Among the most conservative states, the 50% threshhold revolves around "the heartbeat" which starts around 6 weeks but is pretty pronounced by 10 weeks. Some states have tried to outlaw elective abortions all together, but I doubt that will hold up in court when challenged.
I do agree with your statement about the logic of aborting a viable healthy baby, but people are not "logical" or men wouldn't convince themselves that the buying Porsches for their high resale value. People are emotional.
Second, I also agree late term abortions are rare, but sadly to often they are not about medical necessity. They should be even rarer, than they are and involve medical necessity since at this point if viable the baby can live without the mother.