How is it that in the modern day, there still exists a plethora of disputed national borders, even between very wealthy/powerful nations and much poorer ones (e.g. the United States and Haiti, Russia and Georgia)? Why are these disputes not more easily settled, diplomatically or otherwise?

Stepping down from opponents threat and seceding what is considered as a part of your nation gonna faces heavy resistance from your political party, the citizens and your nation will be considered as being weak and easily bullied. Diplomatic approach can only work if both sides are ready to reach a compromise while majority of the disputing cases are one side claim all. It's exactly that a dispute between a powerful nation vs poorer one that led to one side tries to extent its power, giving the poorer one no choice but to fight back with everything it has. Vietnam/Philippine/Indonesia/Taiwan/China vs China/Vietnam/Philippine/Indonesia/Taiwan claim in South China sea is one example. Philippine brought the case to the court but Vietnam refused to back Philippine case because Philippine also claimed the part Vietnam considered as their. Since none of the countries in this case love each and some actually hate the other, it's impossible to reach an agreement.