To confirm this, I recently asked LinkedIn support:
…is there a way to change the order of individual line items in the COURSES section of the profile? The system appears to add new courses to the END of list rather than the start and that make it fairly useless. Perhaps there is a way to set the sort order on that section from newest to oldest.
and they got back to me with:
Currently there is no mechanism that allows for you do what you are looking to do.
You should submit your suggested enhancement via the Feedback form:
This is the best way to make your ideas known to the developers and decision makers.
which is pretty much useless.