I often draw lessons for startups from the world of entertainment. In one episode of my favorite entertainment podcase, the Kevin Pollak Chat Show, Kevin discussed why he thought it was so important to nail the first joke of a movie.
Kevin's point was that the first joke has to let the audience know that they're in good hands. The level of uncertainty is highest right at the start of the show. The first joke lets the audience know whether they're in good hands. A great first joke signals that the filmmaker knows what he or she is doing, and that the view can relax and enjoy the ride. A flat first joke increases the tension, and makes it even harder for the movie to recover.
(Lest you think it only applies to comedies, I think a similar point applies to dramas as well, hence the James Bond films' focus on providing a crackerjack opening sequence, even though it usually has nothing to do with the rest of the movie.)
When you are fortunate enough to get someone to come to your startup's website, sign up for an account, or download your mobile app, it's critical that you let the user know that he or she is in good hands. That's why the fit and finish matters. It's not that it really affects the user experience that much; it's that it affects the user's confidence in you far more.