The US is one of only three countries that allow for abortions past 24 weeks. The other two countries are China and North Korea.
This is just not true. Most Western countries allow abortion beyond 24 weeks in specific circumstances. Here are a handful I know off the top of my head:
All of the examples you cite allow for abortions in only limited circumstances. In the US, it is possible to have abortions for elective reasons. The two are not comparable.
As a moral issue, I really don't see any valid argument as to why late-term abortions should be allowed
So it's perfectly fine for a woman to die from health complications as a result of her pregnancy?
You are referring to edge cases. Most late-term abortions do not meet this criteria. I also understand that there was language inserted into the bill that recently failed in the Senate that used "health complications" as a loophole that would effectively legalize abortions up to the moment of birth for elective reasons.
Any exception that allows for late-term abortions would need to meet a very high standard, such as the requirement that new information was discovered that was impossible to have been known prior to the threshold cutoff, and there being a substantial risk to the lift of the mother.
As a moral issue, performing a late-term abortion because there is a risk of health complication for the mother is doing something that is guaranteed to end a baby's life that merely reduces the risk to the mother's life, when it was not certain that the mother was going to die from the pregnancy.
As a constitutional issue, there is no basis to guarantee the "right" to have an abortion.
So if it didn't exist in Philadelphia, 1787, then it's fair game?
The constitution has a means to be amended if there is the will of the people to amend it. If there is insufficient voter support to amend the consitutition, the only reasonable conclusion is that the people who are governed by the constitution have not consented to changing the consitutition.