Legal Alien in Prague

After pilgrimaging to the alien's police for the third time I've been finally accepted and got a paper about it. I don't understand, why they set up alien's polices at all (not only the Czechs but the Germans and others, too), if their only job is to keep foreign people from staying legally in the particular country: If they want the people not being legal in their country why don't they just leave them alone instead of wasting their time with obliging them to spend their time with ineffective bureaucratic things. They could save so much money, which they could use so much better elsewhere.