This is typical for more recent iOS versions. If you add a shortcut tile to your home screen, the launcher does send specific headers that tell Safari to go full screen. There is an additional fullscreen method that works for me:
Settings -> SEO + Metatags -> Script/Metatags in header
Edit: meta tag disappears on forum, attaching image:
The above allows the browser to go literal fullscreen mode. This is not a good solution if you don’t have back, forward, refresh etc navigation buttons in your app.
I have looked into this before, and there are methods to force this on Android+iOS Chrome browser as well. Worth Googling. If you’re looking to squeeze as much room as possible into the browser, go ahead and play with scrollbar CSS in the same input box:
border: 0px none #2A65B0;
border: 0px none #132A54;