I agree with your logic, but I don't see it applying here. All immigrants are already required to carry proof of their status with them at all times. That's not a new requirement. There's no unreasonable or additional "government intrusion" with that. Period...
It's the slippery slope argument. I'm not going to get in to all the misconceptions about illegals here, it would fall on deaf ears. But, the law gives cops carte blanch to detain folks when they have 'reasonable suspicion' they are illegal. (For the record, being "illegal" in this country isn't actually a criminal offense...it's a quasi criminal offense, and basically amounts to little more than a misdemeanor, the crime is illegal entry...the courts have said that remainging illegally isn't a criminal offense...many get here legally and remain after their visas expire...that less true in the border states, but a fact non the less.) Ok, fine...but reasonable suspicion is a VERY low standard, and this law is ripe for abuse of American citizens who are not, and should not be required to carry proof of citizenship (read as being in my best Nazi SS dialect "Zyur Paperz Pleeez!") being detained for not having proof of something they're not required to have in the first place. I think that's the reasonable arguement here...the potential for abuse is so great.