While there's no blanket requirement to carry ID there is case law that supports detaining people who can't/won't present ID. It's mostly post 9/11 detritus.
I think the subject is similar to online legal resources that tell people they should simply "walk away" from questioning if they feel the officer has no RS/PC.. in reality this would only work after a lengthy process and one might find that police officers choose to ignore both letter and spirit of the law.
Addition: I've been in very few circumstances where you could "set straight" a police officer. If they have already decided how something was going to be done about the only thing that is going to get you out of it is intervention from another officer. No amount of reading legal documents you have on hand is likely to make them snap out of it, on contrary the situation may deteriorate further. This is obviously neither rule nor exception, but something that needs to be considered.
I've been stopped and searched illegally once: I very politely asked what the grounds for stopping me were, and after he had patted me down (still only requires Reasonable Suspicion in US) I asked what PC he had for a full search. Something to the effect of "here's probable cause" was yelled in my ear as he pushed me face first into a wall (handcuffed mind you) 😀 Obviously, I was let go without any charges.. Only damage was to my pride; it would've gone a lot better if I just sucked it up and let them do what they wanted. 😱