I agree that, in 137 posts we haven't got very far, although I don't think it has become completely circular. But if it has, let's try to break out.
We all agree that illegal immigration is a reality, and it is petty damned obvious that rounding them up and sending them home is futile, even if it is the right thing - and the only right thing to do (I said "if"). Even putting them in gaol for a few months before they go home won't stop the others - and probably won't deter the ones who are actually put in prison ... they'll try again as soon as they can.
So what's the answer? Giving police more powers demand to see olive-skinned people's papers and to incacerate those who can't produce them? Allowing vigilantes to patrol borders instead in the hope that their enthusiasm for the job will make them more effective than existing border guards? Throwing the borders wide open?
I suppose that first, we have to agree what the pupose of border controls is, and take it from there. We also need to take an unbiased look at why immigrants take the risks they do for - let's face it - economic reasons.