The thing is that what we see today as relatively "homogeneous" populations is mostly a RESULT of decades of creating such a homogeneity. To stick with a country I know a little (France), one may look today and see it as a relatively homogenous country with regards to its majority population : white, traditionaly catholic, one language. But that is a result of a process over the centuries. France had a sizeable protestant population, which led to extremely bloody internal wars (meaning, among white french people), which explains part of migrations to the Americas (US and Canada) as well as South Africa or the Netherlands for example. So the country BECAME religiously "homogenous" by killing protestants or forcing them to leave (basically they were refugees to use modern terms). Same for language : what is now known as the french language was mainly the language spoken in Paris and by part of the elite. I think that up until the 18th century it was spoken by a minority of people in France, because local languages were still strong and people held to it as a link to their own history/culture. But the french central power imposed (sometimes brutally : speaking Breton at school led to children getting punished) French as the standard, and everything that was linked to local traditions/customs/etc was ridiculed. In a way, you could argue that the creation of the "French nation" meant destroying all the local "nations" that existed on the French territory.
Same thing in Italy. For someone looking from the outside in, it looks homogenous. White, catholic, one language. But in the South people damn near look North African, while those totally at the North look Austrian/German (and speak German). The way italian is spoken is very diverse from one region to another. The current form of "standard" Italian seemingly comes from Florence and the region of Tuscany : that was the center of political, economical and cultural power for a long time in Italy, so it had ways to impose their brand of Italian. But the formal power wasn't as strong as in France, and Italy has a long tradition of "city-states" all very attached to their autonomy : Italy only became a single unified country ("nation-state") in the late 19th century. And those cities were fighting against each other, and to this day there are VERY STRONG local particularities. Rome is not Milan which is not Florence which def is not any place in the south of Italy. Sardegna still has its own language, and they talk about "the Italians" when referring to people from the continent. I speak Italian but hardly understood a word when I went to Sicilia.
So yeah there are nuances : a Belgian is closer to a French than an Estonian is, so it would be easier to build a french "nation" with the Belgian than with the Estonian. Geographical proximity works like that. But it does in no way mean that that Belgian and that French are "homogenous", because I know first-hand (I'm Half-Belgian) how different the culture, values and whatever are in France and Belgium. (I also take that example because Belgium once was part of the French empire and could very well have been part of France, in which case we would have been "frenchisized", "made French" by the same process that happened in French regions. Didn't happen that way, so the differences between Belgians and French remain).
The interest? Power of course. It's much more easy for the rulers to rule in one language, with one central government and with a set of unified rules for the whole territory. Basically it was local colonization. Some countries had a central power that was powerful enough to do so (France) others not (Italy). De Gaulle once jokingly said "It's impossible to govern a country that has 400 different types of cheese"
What he was really saying is that France, in all its "homogeny" (White, traditionnaly Catholic and speaking the same language) is STILL extremely diverse, even without taking into account immigration. Sidenote : As France moved forward, it realized that it was better management to delegate more and more power to local (Regions) levels, and to better take into account local particularities.
My thoughts is that we should do what we should've done all the time : accept the fact that people move, countries evolve, languages are learned, etc. It makes no sense in this current world for any country imo to only teach one language to its children : 2 or 3 should be the minimum. Luxemburg does that already (French, German, Luxemburgish), it's a sure way of opening to diversity as well as a plus on the labour market. We should also accept that diversity is not a threath, and that we are all ALREADY diverse as well. France has had influences and contributions for centuries from Germany, Italy, Spain, Portugal, Russia, Turkey, Northern Africa, England, the US, Muslims, Jews, all the former African colonies...the list goes on and on. Sarkozy's family is from Hungary. Valls' from Spain. Same in Belgium : our former PM is the son of Italian migrants (lest we forget that 60 years ago racism in Belgium was primarly directed at Italians, as people thought "they would not integrate". Same old story). Borders have never and will never stop people from moving around, it only makes it more difficult. It serves no purpose to cling to some kind of "identity" because said identity simply does not exist : it is a mix over various influences that make a country what it is today. France in the 40s is not France in the 80s which is not current France. The EU had an opportunity to surpass all that nationalism, but old habits die hard. It's interesting that most "nationalists" now (Extreme-Right or not) cling to something who itself is a political construct. There's a reason that the term and the process of "nation-building" exists : it implies that nations are built, it's not something natural. So if it's built, then you can choose to build something else. But like I said, we are all so stuck in our habitual frames of thinking that it LOOKS that it's impossible to have something else than nation-states. Euro countries, especially France, missed an amazing historical opportunity : we are historically and culturally linked to North America, historically, culturally and geographically linked to North Africa and the Middle-East, historically and linguistically linked to half of Africa. Why turn our backs to all of that? All because of the fear of diversity. And then they lament the fact that France has lost influence in the world. No shyt.
Anyways I think we are at the end of the nation-state framework as we know it. It has never really worked anyway, and there is a big push towards federalization and respecting local particularities. People travel more and more, have access to other cultures, whatever. I'm Half-Belgian Half-Centralafrican, grew up in the US, CAR, and teh country I know the most is France. Which "nation-state" am I part of?
There is a lot of talk in France about how to reform the institutions in order for them to be more in phase with what is actually happening on the ground. New forms of doing politics are being experienced at the local level already. And like the wounded lion, the fact that Extreme-right and nationalist parties are being more heard is a direct reaction to the fact that the world is changing in a direction they don't like. The problem is that it's much easier to defend a crumbling system than to build up a new one.