Kudos to her for putting herself out there, but she's misunderstood what the point of this kind of application is.
When you make a grab for a job like this, you underscore the fact that employers don't always know that there is something that can be improved - and that someone should be hired to do it.
I vaguely recall someone writing an application for 37signals, where he made some redesigns for the site that he thought were needed. (He made them - actions speak louder than words; deeds are better than words; show, don't tell.) In other words: "You need to improve these things - guess what, I can fix those problems for you." It must be what every start-up dreams of at night.
This is what these applications are intended to be about. Again, kudos for putting herself out there (I shudder at the thought of putting myself in the spotlight of the internet with my identity displayed and available for public mockery). But the application itself is very vague and will do little to convince the guys at Instagram to hire her.
I mean, who the hell wouldn't have an interest in working at Instagram? You are not a unique snowflake to have that desire - and it makes the attempt to convey passion less persuasive.
But hey: the site currently has 70 points on the front page of Hacker news, and a lot of new people now know her name. It's inconceivable that there is any "bad publicity" to come of this, so she can't really fail, regardless of what happens from now on.