You're implying there's a kinda choice, that things can be sped up by acting quicker locally. This squarely refers back to the potential bottleneck mentioned above.

As a general rule, elements despised in one society for being unruly (to call it that) are probably unwanted in most societies. For this point alone, hardly any country should be expected to welcome people who are unwelcome here with open arms. Or support/enable a speedy deportation process.