Culture is deeper than food and music. Have we taken any sort of political, economic, legal, or social systems/theories from natives or blacks? And if we have, can it even match what we've taken from Europe? We are a republic, loosely modeled after the Roman Republic and couched in Enlightenment principles. We are a (mostly) capitalist economy. We use a law code derived from English law, modified by us throughout the years. Our philosophy is decidedly Western (shout-out to pragmatism!)
If tomorrow I woke up and all the hot dog stands closed down and were replaced by kebabs and falafel, and all the rock bands suddenly changed into bands that play the didgeridoo I wouldn't particularly care. But if I woke up and instead of common law we had Sharia, I'd be very concerned. If I woke up and dog meat was a popular food item, I'd be concerned (I view dogs as friends, not food, just as Hindus don't view cows as food). If traditional western norms of beauty changed and suddenly lip plates were all the rage, I'd be disgusted. Is having Shariah, dog meat, and lip plates inherently bad? I can't particularly judge, but I would never want it to replace what I know and love. This is the culture that matters, not what you eat or how you dress or what's on your country's flag. Just about all, if not all, of our deep and important culture is what I'd call "Western". This is one of the reasons it's easier to integrate Europeans than other groups. Eating a hot dog and loving rock doesn't automatically make you an American, just as liking anime and sushi doesn't make you Japanese. I won't deny that some (but not all) of our surface culture has been touched by diversity, but it doesn't really matter. As our white European majority sinks from a majority to a plurality, it's entirely possible that our deep culture becomes affected.
"You seem to be way focused on actual breeding for some reason"
The reason, quite simply, is that's what matters. That's what ethnic diversity is. It's what decreases trust. It's what engenders hatred and it's what starts wars. You may think it illogical, that we're all together, united, in The Brotherhood of Man, but me simply saying "Okay, race doesn't matter", or even genuinely believing it, doesn't make it not matter. It's not going to make Turks and Kurds love each other. It's not going to ease tensions in the Gaza strip. It's not going to solve anything, and blinding yourself to it will only create more suffering. This is because this is how we evolved. If we are not vigilant, I fear the modern humanist West, as a whole, will be destroyed, because we are quite literally inferior, evolutionary speaking. But that's neither here nor there.
"Color isn't diversity, different thoughts are. And people from different places tend to have slightly different thoughts."
At best, then, ethnic diversity is a weak proxy for intellectual diversity. Why even have the middleman of ethnic diversity, with all the cons that brings? Were we seriously lacking in intellectual diversity prior to 1965? Was it worth gutting our societal trust? I don't think so, not by a long shot. The exchange of ideas does not require you to have 35%+ of your population a different ethnicity from you. As you say, Japan got a lot of shit from the Dutch, and all the Dutch had was a tiny island, and they weren't even allowed off it. They never made up even .1% of Japan's population, yet they influenced it immensely. This is exactly why trade is so good and essential. You get to experience the appealing parts of different cultures, without actually having to live among them. You can have your cake (or tempura) and eat it too.
As for the state being powerful, yes, that's my point, diverse nations NEED a strong government to keep order. Homogeneous ones generally don't. I don't wish to live under an empire.