I disagree, any candidate worth having would enjoy such a test. Any programmer who is put off by being asked to program needs to find another profession, period. You should not ask someone to program during an interview, you should review the code they've submitted and make them explain it, all if it, their design choices, their idioms, naming conventions, etc. If they can't discuss code they just wrote prior to the interview, you don't want them, but many good people don't perform well under the pressure of an interview so you won't get an accurate feel for them if they program at the interview.

No one but a programmer is qualified to evaluate another programmer, HR and recruiters have no place here and they'll just waste time and effort pretending to be useful, they aren't.

By doing the test you've already filtered out the wanna be's so you don't need phone interviews, the submitted samples should go strait to a qualified programmer, it'll take him only a few minutes to toss out any bad submissions and he'll quickly know who's worth actually interviewing and who's not.

Code is the only resume a good programmer needs.