Whiplash is from your head moving more than your neck can compensate for. The headrests are designed to prevent excessive backwards movement of your head to help your neck not get completely over-extended. Heads are actually quite heavy and there are a lot of very important things inside the neck that you don’t want getting fucked up be getting jerked around too much. The muscles in your neck can only do so much in a high-velocity situation like a crash.
I’ve played Judo, and I’m a licensed EMT, and I’ve worked in ERs, and I’m a third year medical student. I am quite confident in telling you that you are incorrect. Modern safety standards make it so that the seatbelt locks in a crash and limits your longitudinal inertia. Also, many dummies (and actual humans I have cared for) have “hit their head wrong” on the headrest due to their height, posture, or position, and they don’t break their necks. Did their scalenes, paraspinal muscles, and sternocleidomastoids hurt like hell? Absolutely. But they didn’t have broken necks.
Your body can compensate for a lot, but it was the introduction of headrests in cars that has been one of the biggest contributors to the drastic reduction in fatalities. The point of the headrest is the same as the seatbelt: to limit the range of motion your body goes through in a crash. Seatbelt signs and headrest concussions are real things that can cause some pretty significant problems, but those problems are easier to fix when the patient isn’t dead or quadriplegic.