Earlier quoted context omitted.
This rests on the assumption that immigrants "deplete systems" and that citizens don't. They're both just people. If anything, immigrants are generally above-average in terms of dedication (for one, there's a sampling bias because they've just travelled across countries to come to yours). Limiting access to contributory systems (e.g. having a state pension require contribution) is reasonable, preventing someone from…
The visa-regime borders are not mutually exclusive with migration either. Actually, it ensures, that the country gets the well-driven ones. If you want to see, how to destroy a country fast, have look at the UN Global Compact for Migration. Social service-wise, it binds the countries to provide more for immigrants (even those entering illegally) than for their own citizens!
I'm curious what you mean by this: either, a) the compact has language to the effect of "You must provide better services to immigrants than your own citizens." OR, b) the compact requires X standards of human services for immigrants and many countries don't even currently provide those standards for their citizens? Or something else?
a) seems very unlikely.
b) would make sense since a migration/refugee compact naturally wouldn't have standards about general citizen human service standards. Plus, if the compact does specify a basic level of human services, many countries, especially the US, already don't meet those standards for their citizens.
Either way, that doesn't provide any evidence that net immigration "destroys a country fast."