That might have even been true decades ago when rates of influx were tiny, but now we live with a firehose under the assumption that there cannot be any hysteresis — we are a big planet, any new culture is a point mass. And that all these new populations get along (they don't).
We invaded Afghanistan and started nation building on the assumption that within every Afghan is a Western liberal trying to get out. If you haven't seen it, please watch the Adam Curtis doc "Bitter lake" to see how much of a disaster this project was. We don't understand their culture at all.
Those same people who planned that war brought about the current normal of historically flows of people every year. Some of them have explicitly said they wanted to do a cultural transformation project too but I'm prepared to say that was a relatively small group of extremists.
Most of the world is very, very, different to the things westerners are used to. We don't have clans, we don't marry inside our families, we don't grow up wanting to make our parents proud anywhere near as much as in non-western countries (etc, "WEIRD" culture as argued in the now-famous book).
Not all non-western countries are the same e.g. SEA famously quite compatible with our culture up to a point, but you'd clearly give a daughter very different travel advice if she was going to Morocco versus Inverness.
If nothing else, is it not a bit weird to go to quite a few large European cities and find roughly the same distribution of people serving your coffee or waiting at your table?
I genuinely wonder what the many Chinese tourists coming to London think when they go into a shop to buy some water or something and all the staff are new arrivals to Britain speaking (say) Hindi rather than English to eachother.
And that's not to say they couldn't integrate at some point but at the moment the "purpose of a system is what it does" revealed preference is that we don't want them to.
Also, this conservative thing of being bothered by people speaking a language they don’t understand amongst themselves shows the eternal entitlement they feel. Everyone’s actions must cater to me, I must understand and be able to participate in everything I want without having to do anything extra.
It’s like people visiting the countryside in Brazil and expecting to find English speaking restaurant servers everywhere.
> This is really only a recent western dalliance too
Historically, it's the opposite, homogenous populations are a very recent thing.
> "What does it mean to be British?"
Doesn't mean much? There's Wales and Scotland right there, you go to Spain and find the catalonians, basque, gallegos. A country is very rarely a single thing, its a mix of multiple people's and trying to come up with a single storyline for it is a very modern thing.
People identify with the city and region they're most associated with, I'm Brazilian but first and foremost I'm northwestern, the culture, accent, food, customs and religion there is unlike other places in the country. I see no reason to find an answer to "what does it mean to be brazilian" because different people will have different answers for that but if I meet someone from my region we will quickly connect on our shared experiences.