Is a world without any borders a good idea?

Nation-states maintain borders for safety, maintaining political jurisdiction. Yet, some forms of open borders exist between nation-states: the Schengen Agreement in the European Union, borders between India and Nepal, Ireland and the U.K., and the CA4 Border Control Agreement in Central America. Most nation-states maintain strict border controls, restricting travel between countries and barring entry to migrants. Millions of people risk their lives trying to cross borders into other countries. Some are fleeing violence and war; others are looking for better economic opportunities or to be reunited with family members. Borders protect but they also actively promote death and suffering, as seen in the strategic placement of border patrol along the US-Mexico borderlands. What are the possibilities of a world without borders?