Many good candidates could be put off by such test. More importantly, even if they agree to your test and send you some code, you need an engineer's time to evaluate the code sample, and if you're going to invest engineer's time you might as well do a full phone screen. The recruiters are by and large non-technical people. They would love to be able to ask some technical questions which could help them predict whether a candidate would pass the interviews or not. I've been actually asked by a recruiter friend of mine how to do it. But, if you think about it, this is not so easy if you're not a programmer yourself.
You are absolutely right that it would be madness to hire a programmer without having seen him code. The companies are well aware of it and they will surely ask you to write a lot of code during the interviews. But that comes at a much later stage, as it costs them much more money than checking on your resume whether you have a degree or not.
I'm not saying that I like the way things are, but that's just life. If that's of any consolation, in most other industries the requirement of having a degree is much more strict than in case of Software Engineers.
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.
One issue to be aware of is that it's not just the corporation interviewing multiple candidates. It's also the candidate interviewing multiple companies. Putting a large burden on each candidate may not scale if every company does it. I agree that it's important to assess actual coding ability but I don't know if a programming test is the best way to go about it.
Any programmer who considers such a trivial test a large burden, you don't want. There's no other way to assess programming ability than programming, it's really that simple. If you hire an unknown programmer without making him submit a code sample, then you deserve what you get because you're gambling and likely to lose. The whole point is to find good programmers, and good programmers enjoy programming, they'll happily write a trivial program to prove it, happily. Anyone who balks at such a test is not someone you want to hire, period.
You are absolutely right that it would be madness to hire a programmer without having seen him code. The companies are well aware of it and they will surely ask you to write a lot of code during the interviews. But that comes at a much later stage, as it costs them much more money than checking on your resume whether you have a degree or not.
I'm not saying that I like the way things are, but that's just life. If that's of any consolation, in most other industries the requirement of having a degree is much more strict than in case of Software Engineers.