The reason I carry ID and car keys is primarily that trailhead car clouting is pretty common in my region. I therefore want to leave no clue to my ID in the car. I strip my ID down to the bare minimum before I leave home, including leaving off the pushbutton gizmo on my car key. What I take is drivers license, auto insurance card, car registration, one debit card, one credit card, car key plus a small slip of paper with emergency info including my health insurance info. This all fits into a snack-size sandwich bag and weighs about 2 oz. (half of that being the stupid key, which contains electronic gizmos needed to start the vehicle). My pack has a plastic ID pocket at the top, which contains the stuff. I treat my pack as though it were my purse and don't leave it alone, unless I take the ID and stuff out and put it in my pocket.
My understanding is that while US citizens are not required to carry ID, we can be required to identify ourselves to law enforcement when requested, which sort of makes the question moot as to whether we're required to carry something! Note, however, that those who are not US citizens are required by Federal law to carry proof of their legal status at all times while in the US--passport or green card or whatever. This has been Federal law for many, many years, and is the law in most other countries, too.