That's why it shouldn't be the first step of the interview process, but it's totally fine as the last step. When the hiring party thinks: "we want this candidate if they're as good as they seem to be", then it's a good time to have a look at their code.
Is it really normal for a developer to need to apply to that many positions to find a decent match? I've only ever done a dozen or so at once, and each one I spend a decent amount of time researching the company for tailoring a cover page (if they accept them) or for the interview. I find those making the hiring decisions are quite impressed by candidates who have done their homework (and more than once I've made the hiring manager a bit worried about how I found so much information just through google searches; they don't realize how much their employees let leak through Linked In resumes and such).