Good point. And I would seriously consider an applicant that wrote such an application, but better than putting it in his resume would be to write a quick note.

Good point. And I would seriously consider an applicant that wrote such an application, but better than putting it in his resume would be to write a quick note. "Hey, I've been looking for a new role. As part of my process I wrote this app. See it here and let me know what you think." That would get somebody noticed.