> A large part of what makes the first world so productive is its culture

In view of history including colonialism this statement sounds very naive indeed.

Eh, you don't need to dismiss the impact of colonialism or have any notion of inherent racial qualities to think this is true. Having strong, consistent institutions and relatively low levels of corruption (or at the very least, concentrated and generally legal corruption) is a per se advantage of operating in a developed economy. If you don't have experience with the other side of things, you probably don't have a clear sense of just how gummed up the works can get with nonsense.

I can't prove that there is no limit to how many migrants the first world could absorb without losing the rule of law, but it's pretty obvious that if there is such a limit it's higher than the status quo!

"economic migrants" need almost zero training. However, I do agree that this will put pressure on already complacent welfare system, or group of people and may cause new economic, social regrouping, wealth distribution etc. To provide services, one would be incentivized to integrate.

> On can't/rarely provide services and choose not to be aware of local customs/traditions. [...] To provide services, one would be incentivized to integrate.

It is completely possible to provide services without integration in insular communities, which tend to appear when newcomers come faster than they can integrate.

it's absolutely possible to spend whole winter in a thin cotton shirt, but most of us prefer not to do.

>To provide services, one would be incentivized to integrate.

Only as long as one doesn't have a sizeable presence in the host country.

I disagree. Incentive to get recurring business mandates integration. Also, if the presence is not sizable enough, they would largely go unnoticed, so, integrate or not, it doesn't matter.