Guarantee you if we magically eliminated borders world war 3 would erupt the next day as countries desperately redraw them.
Good idea in principle, but not feasible in this day and age. Humans are simply not sociologically advanced enough to sustain that kind of political venture. For starters, humans produce more than enough food to feed the world and yet food insecurity is rampant even in countries with excess.
Open borders will happen when the rest of humanity's shit has been sorted out, not the other way around.