Waiting for enlightenment in global village I think is a lost cause, we can barely even take care of ourselves yet. Us-themming has its roots in the evolution of our species, which makes sense looking back millenias in the past, but I think it is nothing more than a neighbourly extension of kin-selection. I think we needed to craft certain kinds of iron-age myths and beliefs that forms cultures and traditions to control thousands even millions of the members of our society and we feel the need to preserve them, so to succeed, we create borders as to not let wandering Janes and Joes who we deem as aliens enter our turf. Imperial expansion and resource allocation is also a major contributor to this global monopoly and in some cases, it's driven by our own collective narcissism.
Borders I think is founded in trust, without the concept of borders, we'd still be trying to expand our realm by waging war with each other for whatever reason, even with this we're still trying to broaden our backyards bit by bit by creating "china towns" or any form of seclusion within a foreign land.
So to answer your question, borders can be necessary if it's main purpose is to filter out people who we suspect will cause disorganization, but not necessary enough to welcome change, if these migrants are adaptable then there will be no need I think, but then again this entirely depends on what kind of upbringing they have and what practices or culture they grew up in.