That's partially true; the bit about borders and human history (so long as you sequester 'history' to 'recorded history') - but nationalism is actually newer than you'd think, and there were human societies for thousands of years before there were borders. More recent if you go by the current definition of border (formalized, surveyed borders are also relatively modern).
Is nationalism going to peter out? No, of course not. Do some people care for reasons that are important to them? Sure, I don't want to tell anyone how to feel. I am just another jerk with an opinion like the rest of us.
But if you were to ask me, it's take it or leave it. I'd be more than happy to see free movement in the world. Just another set of rules I'm not using.
Yes, hard borders are far more recent than people think. As late as the First World War you could travel the world without so much as a passport.
But: back then only a handful of very rich people had the means to do that, and taxation and social protection were much lower than today. Those things are related. They (IMO of course!) are what make borders a pragmatic necessity.