Where to start....
Honest cops, I used to believe they existed. But I've been terry stopped when obviously not up to no good. Unless you count walking home down a well lit street wearing jeans and a tee-shirt as reasonable suspicion for anything. Cops aren't there to prevent crime, they're there to make arrests after a crime so yes they can sit there with their hands in their pockets.
And what is a good reason to believe you're in the country illegally? The same standard for Terry stop? None since they can say anything and there's no way to refute their claim?
There's no law requiring me to carry ID, so why would I want to hand it over to cops? The burden of proof is on them, not me. Why should I be expected to roll over and prove myself to every cop who happens to pass by and decide they have nothing better to do than harass me?
Demands based on suspicion just won't work. There's no practical way to deal with abuse and you know full well that if you have humans, you have abuse. At the very least we need to use a probable cause standard.