Responses:
DK-Prof, As you have acknowledged, you already, under penalty of perjury, supply your current address to the IRS each year. I propose this info be instantly supplied to the INS. In addition, I would also require all aliens, green card or other, to report their residence annually, on or about Oct 15th, this info directly to the INS. If your official or primary allegiance is not to the US, then the US has a vested interest in maintaining a limited watch on you. Sorry if that offends, but many other civilized countries do much more than that, such as requiring you to surrender your passport, etc.
Rug00red and Mean-Green: I support dramatically limiting the total number of legal immigrants admitted to this country annually. Seems to me that a combination of your two approaches would be more effective than either seperately.