That's a beautiful globalist elite fantasy, that really couldn't be further from the truth though. You're wrong on all points. Most countries around the world clearly still maintain their "default" culture. Waltz into some non European countries and tell them that, you're in for a surprise. All European countries still overwhelmingly have unique native cultural identities, these cultures created and maintain the societies and political environments that are so desirable to people around the world. When you give up that successful culture in favor of misguided liberal philosophy the country you knew will cease to exist, it will become another society to flee.
I don't understand why you seem to desire a scenario where your culture is constrained, and has to adapt or get out of the way? 
This really doesn't affect me, I'll have the ability to enjoy the Anglo culture I was born into for the rest of my life. When I explore new cultures it's voluntarily.
Not sure if you get my point, so to clarify things: this is not a 'wish', this is the result of the dynamic world we're living. This mixing process started during the first colonies and it's speed went through the roof during the last 100 years.
Yes, you're correct that many so called 'cultures' hang to 'their' roots, call it nationalism. To me this is simply a tradition that gives people a false 'united feeling'. If this gives them a good feeling, more power to them, but they're delusional. Keep in mind that these cultures are dynamic; they change over time. This was a very slow process for centuries, but not anymore.
Some traditional people may worry about this, but it won't help them. This strong mix of processes can't be stopped, since we're with so many 'cultures', religions, political ideologies and so on.
Again, I'm not saying this is what I wish, though it's interesting, this is simply the reality.
