I think you'll have traction problems on the developer side. Doesn't matter what kind of job it is, you can be pretty much 100% guaranteed that the job will be listed on the company website without any of the extra hoops to jump through. Requiring someone to build a web app just to apply is a huge requirement. It's fine if you gave someone an interview, and this is the final step before you hire...but requiring someo…
I can see this as a useful tool for pre-phone screen or post-phone screen evaluation. At the startup where i work we do send the candidate a small code problem after the phone screen and before the on-site interview. I know lot of companies do that. Gives you a little more insight about the candidate and also ensures that you are not wasting your teammates' time as well as the candidate's time.
Also, submitting the resume/github link along with a solution to a programming challenge increases the probability of getting to the phone interview stage. Highly applicable for famous companies like FB or twitter where they receive hundreds of similar applicants every day. Of course it is a stupid method if you are trying to hire a team lead or senior engineer but for fresh graduates or junior developers it works well. I don't think they will mind spending an hour solving a problem.