On iOS, using AppBarBehavior.scroll can cause the status bar overlay to go from being painted over a dark background to over a light one (or vice versa). Doing so without calling SystemChrome.setSystemUIOverlayStyle() will mean that the status bar will be hard to see in one of the app bar states (either visible or scrolled off).

e.g. in the Flutter Gallery's contacts demo:

App Bar visible

App Bar scrolled away