why are the leaves at the farthest part of the branch the last standing still?

its the "apical meristem"

most of the actual growing happens there

IAA indole acetic acid and kinetin are flowing there, that affects the formation of the abscission layer which forms causing the leaf to drop

Because, just in real life, the leaves are the youngest and has more days to go before they die.

More in the biology- the cells of the youngest leaves at the topmost are more actively dividing. In a sense, more robust and has more staying power. Or, the route for nutrient delivery is more direct -axially - as shown by the cross section of the tree trunk or branch which means at the tips the route is more of a straight line which is the shortest route.

Or, it is not entirely outlandish to assume that the "end" leaves have a time clock or that the leaves have chemicals like an antifreeze, that are present in greater quantities to protect them.

The time clock is determined with the formation of chemicals that start the yellowing of leaves and finally the stages of separating the leaves from the branch at the point of contact. see end of leaf stem.

There is more chance of leaves in the lower parts of the tree brushing against other leaves as they fall, causing them to fall sooner. The highest leaves never get hit, so they stick a little longer. Just a suggestion.

maybe because they are the youngest, last in last out?