If we want to get rid of national borders, first we need to standardise wages and taxes throughout the world and have just one world currency worth exactly the same in every country. This will reduce the problem of people migrating on mass to the richest country at any one time and the devastating effect that would have on the infrastructures of the nations. But this would come at a huge cost to most people in the developed world. If all the wealth of the world was distributed equally among all people (men, women and children) we would have about $9000 each. Are we prepared to cut our coat according to our ideology?
Another problem for Western liberals would be a cultural one. I doubt that unrestricted migration of Latin Americans into the USA would undermine any of the freedoms and equalities that liberal America has won over the last fifty years; in fact, some Latin American nations are more liberal than many American states. However, what if people from areas of the world where the cultural/religious beliefs differ greatly from those of liberal, "Christian" westerners, were to enter the USA (for example) in such numbers that their votes meant the overturning of the human rights legislation that liberals have fought so hard for? True freedom of movement would allow for the possibility of this happening.
Basically, are we prepared to put our money where our mouth is? Are we prepared to lose our freedom to win freedom for everyone?
Please note, this is not an attack on anyone. It is a question to myself really. Personally, like, I expect, most on the left of politics, I want my cake and to eat it too.