Until I hired a piano teacher recently, I hadn’t fully appreciated the importance of staying in motion while playing. It’s odd, but you really can hear and feel a difference in the quality and character of the music when your hands are only in motion as you strike keys versus being intentional about keeping something moving at all times, in all those tiny (or sometimes not tiny) in between places where you aren’t specifically striking a key.
It’s especially useful for pieces like Mozart’s piano sonatas, where the sustain pedal is rarely or never used, because the music can still be made very smooth and uninterrupted without using the sustain pedal. I’ve heard my teacher and some pianists on Youtube refer to this type of playing as being exposed, i.e., you cannot hide behind sustain or other notes, so details like this can be extremely important for repertoire like Mozart’s sonatas.