Allotting borders based on straight lines based on latitude or longitude can lead to trouble. Let's say that Town A and Town B are on the same side of a mountain range, and Town C is on the other side of said mountain range. Towns A and B speak the same language, but not the same as Town C, or there's a cultural difference, but a straight border is decided by two governments that goes at an angle to the mountain range, bisecting the area so that Town A is on the same side of the new border as Town C, but not Town B. The trouble here is that Town A feels more of a kinship with Town B than Town A.
The only thing that's going to change National borders, is an army. No country is going to give up there land or risk giving it up to their neighbour. That said the reason lines are used on a map is because that's the only way governments are willing to divide the territory, Natural formations mountains and rivers are for the most part in one nation or another, there not in the right place to always be used. So short of a war your not going to change people borders by asking nicely.
If i were in charge of redrawing the worlds borders, the number one thing that would determine borders would be the people in the are. Take Kurdistan as an example. Kurdistan is an area in the middle east that is divided between four different countries without their own despite the Kurds sharing language, religion and culture. They are currently fighting and have been for decades to redraw the borders without much luck other than their autonomy in Iraq. If the borders of the countries involved did not include Kurdistan when initially drawn up, millions of lives would have been saved and a handful of conflicts wouldn't have happened.