Understanding image display on a TFT/LCD display
As you say, E-ink displays are inherently static. Most other display technologies are not inherently static1, and must be refreshed in order to prevent the pixels states from being lost.
In LCDs, the pixel intensity is determined by the charge on a thin-film transistor embedded in the display panel. This charge leaks away over time. Also, LCDs must be driven with an AC signal (the polarity of the charge must be reversed periodically), which requires refresh logic.
In OLEDs, the pixel intensity is determined by the current through the OLED. Since it isn't possible to run millions of different currents simultaneously, the display is multiplexed, which again requires refresh in order to create the illusion of a static display.

1 There used to be a technology called &quot;AC plasma display&quot; that is inherently static, but nobody uses that any more. Mechanical flip-dot displays are also static, but they are slow and very low resolution.