I love this movie and I loved the book, but this scene is not one of my favorites. While I agree that Alex has to be humiliated here to indicate that he's no longer in control, I think Kubrick added this scene (it's not in the novel) largely to pander to the youth audience at the time.
With the Vietnam War only just starting to wind down, this scene was deliberately shot to mirror an "induction physical" for a draftee in the U.S. Army. In other words, Alex's nightmare is that of all able-bodied young American men at the time. It's sort of a cheap way of saying that Alex is "one of us," i.e. just another hippy dude being hassled by The Man, instead of the one of a kind psychopath he really is.
"Your next challenge is always your biggest." Joe Namath
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