Since when is it called a "hamburger menu"? I had no idea what it meant until actually reading the article. Names for generic things should be able to convey their own meaning. It smacks of trying too hard to be a person who coined a phrase.

My app has more than 4 views and one of the views needs to have as much of the screen available to it as possible, because a big chunk of the screen will be taken up by the keyboard. One menu button is better than trying to fit everything into 4 or 5 screens and having 5 buttons constantly taking up space at the bottom of the screen.

And I don't think that's "rare". It might be "rare" if your conception of apps is Facebook and SnapChat, but there there is a huge gap in the market for apps of real value that enable users to do real work in ways they can't do with a larger computer. Apps focused on helping users do work rather than selling ads to users will probably always grow in features over time. You can't get all of that to fit in 4 or 5 screens.