I’m wondering about the right or possible interpretations for the “I don’t want to know…” construction when followed by questions.
I’m not a native speaker, but in my own hypothesis the cause of “don’t want to know” can be the speaker’s or the subject’s ignorance, or existing knowledge with regard to the answer to the question. So for the sentence , there are two possible interpretations (a) and (b):
 I don’t want to know who came.
a. because I don’t care!
b. because I already know! Why are you telling me this! (e.g. I feel ashamed that people have assumed that I didn’t know who came)
Does this fit your intuition? Thank you!
As a semantician, you must know that grammar often implies basic semantics. Thus I don’t want to know has the syntax of a denial, which carries a basic interpretation. The full meaning depends on the context, what I believe is often called the frame. Here are few off the top of my head:
Client: Do you want to know what happened?
Lawyer: I don’t want to know what you did.
This is straightforward request to remain ignorant. In the US, a
lawyer is not permitted to let his client testify if the lawyer
knows the client will perjure himself. By remaining ignorant of the
facts, the lawyer may put his client on the stand with (his own)
impunity. Obviously there many reasons to remain ignorant, including
avoiding discomfort, maintaining disinterestedness, etc.
Parent (to child): Go outside and play. And I don’t want to know what you’ve been doing unless you’re bleeding severely.
This is clearly hyperbole. It’s a parent’s request for a little
peace and quiet.
Mary: Do you know how much you had to drink last night?
John: I’m so hung over that I don’t want to know how much I drank.
This is facetious. John probably has a very good idea of how much he
drank from how bad he feels.
A: Do you know that today is the first day of the rest of your life?
B: I don’t want to know what your theory of life is.
This means that B isn’t interested in A’s cliched approach to life.
Context is everything, and I’m sure you can multiply the meanings.