The US went from 87.9% white in 1900, to 72.4% in 2010 [2]. Unfortunately, I couldn't find such demographic histories for other countries. But search for "US/Europe becoming more diverse", and you'll find countless articles, from mainstream publications, asserting this. So to claim otherwise is extremely fringe.
And there is mathematically no way for a place to be becoming more diverse, while keeping historically constant migration. If the migration hadn't changed in some way, then it would already be diverse. It also means that, if it's becoming more diverse, that it was less diverse, i.e. more homogeneous, in the past.
Looking at the present, China is 91.6% ethnically Han [3], and Hungary is 93.5% ethnically Hungarian [4]. So unless you think China or Hungary or US in 1900-1970 are "the most remote parts of the world", then no, homogeneity is provably not a fallacy.
So yes, "People have been migrating from place to place for all of recorded history", but both the rate and nature of this migration changed, and just a quick glance at the headlines of virtually any news source is enough to tell you this.
[1] https://en.wikipedia.org/wiki/Immigration_to_Sweden#History
[2] https://en.wikipedia.org/wiki/Demography_of_the_United_State...
Do you have sources to back this up? And how did those countries become homogeneous, then?
And, modern nation states are very new. For example, France drove to extinction or near extinction all languages besides French spoken in what is now present day France through government policy. Like the language of Bretagne.
Your profound misunderstanding of history is not something I can rectify with citations. Read a book? Like, a scholarly book.
Well that would be a giant step back from all the gains that have been made post WWII with the development of the United Nations, UN Security Council, UN Charter, and the entire body of international laws which is founded on sovereign nations voluntarily subjecting themselves to these international law, treaties, customs and norms.
Why will future generations be interested in things that never existed?