First off, 'reasonable suspicion' is what is being addressed here (ref: Terry v. Ohio, 1968), and while you claim that reasonable suspicion is 'somewhat loosely defined' and go on to defend how it will be used for the greater good of the public, nowhere have you made mention of the negatives, which are pretty worrisome. The new Arizona law does not directly implicate the court case, anyway. It only requires Arizona state and local officials to investigate a person's immigration status in the course of a lawful encounter. Such an encounter might be initiated by the suspected undocumented immigrant himself, rather than the official, but we can agree that more often, suspicion about immigration status will arise in the mind of a police officer after he has lawfully stopped a suspect. The Fourth Amendment from Terry v Ohio already requires that the police officer have an reasonable suspicion of crime to make the initial stop, but the new Arizona law adds on something additional. If the officer develops a further reasonable suspicion that the detainee is an undocumented immigrant, the officer then must take steps to determine the detainee's immigration status.
Should an officer's hunch be relevant here? No. Hunches are only as good as the base of experience on which they rely upon. A person who has had numerous opportunities to sort undocumented immigrants from persons lawfully present in the United States might develop an ability to suspect and detect them. But even then, shouldn't we legitimately worry that skin color and accent would often play a large part in triggering the agent's hunch? Furthermore, Arizona state and local officials who lack training and experience sorting out undocumented immigrants would likely lean even more heavily on such factors.
Of course there will be some circumstances that objectively give rise to reasonable suspicion, even without considering race or accent. A police officer stopping a speeding minivan on a known alien-smuggling corridor and discovering twelve passengers crammed inside, all lacking identification, would of course be a prime example of reasonable suspicion. It's such an obvious case, and it would satisfy the requirements of probable cause. But the Arizona law applies in numerous other contexts as well.
I think that the critics of the new Arizona law are right. The core problem with the obligation to investigate on 'reasonable suspicion' that it places on state and local officials is that there are very few if any outwardly visible signs of immigration status that could give rise to reasonable suspicion in the first place. That's true regardless of whether the officials act on reasonable grounds, or on the basis of a hunch informed by less reasonable grounds. Whatever you think of how "reasonable suspicion" has been defined in the federal Fourth Amendment context, its use in the Arizona law is problematic here.