Nationality is really just a legal construct, anyway - it allows a body of people (known as a 'government') to determine what rights and responsibilities you have by virtue of being in a particular physical location.
I think that most people have a stronger affinity to a culture - especially the culture they grew up with - than they do to a nationality, since culture evokes a more emotional response. Of course, for many people, the two are the same - but if you're a naturalized immigrant, they are two very different things.
Nationality will become even less important to people if more countries start trying to attract people to live in them (for economic or social reasons), but I don't see happening for a long while yet.