Fog Creek does this for inexperienced roles, they have a simple challenge of extracting a string from a text file of garbage and then using that string as the subject line when applying. Took only a few minutes using sort piped into awk to finish it and I'm sure it probably weeds out a lot of applications.
I personally won't do any coding challenges without at least an initial technical phone screen. It's not really fair to ask for that kind of time investment from candidates without being willing to reciprocate.
Fairly giving them a time investment of 30 minutes (reading CV, tailoring technical interview, answering questions) would mean 200 hours of productivity loss. There is no way to defend this to a company, especially when hiring more than 1 a year.
If no coding challenge then it all comes down to the CV. You'll miss out on promising humble candidates who lack the CV buzzword bingo, and get burned on mediocre candidates whose parents paid for them to go through a top university. That's not fair to the talent either.
Of course if someone completes the coding challenge, you give them the time investment they deserve (8-16 hours spread over multiple employees). You save this time by declining those that do very poorly on the challenge, or refuse to do it out right.
You may not have an idea how awkward and depressing a technical phone interview is with a candidate that is not suited to the role. And delegating this to HR/Recruiters is a surefire way to increase noise and crash the hopes of people who pass the screen, but fail badly on future interviews.
I find it way easier (for me as a candidate) to do a quick test than finding/researching/applying to a new company, so if it 2x or 3x my chances it's totally worth it for me.
Finishing the challenge on itself will be the first filter; then you can review the ones who finished it and interview the ones you like most.
BTW if you are looking for a remote web dev (front-end or back-end) drop me a line "public at francisco.io" <= my CV.