Why LED screens have to twinkle?
It's just not feasible.  In a full HD display panel, there are 1920 x 1080 x 3 = 6,220,800 pixels.  That would be over 6 million wires to connect each one to a drive circuit.  And 6 million pins on the panel.  And 6 million drivers.  It's really not possible to build.  So what they do instead is multiplex - row and colum wires with a pixel at each crossing.  This brings down the number of wires required to 1920 x 3 + 1080 = 6,840.  That's much more reasonable.  This nicely maps to the video signal, which arrives one line at a time.  

Generally the way the pixels are built on an LCD screen is there is a transistor patterned onto the glass for each pixel, and then each pixel looks like a capacitor.  The screen ends up looking like a write-only DRAM.  The capacitance of the pixels will hold the level between updates.  In an LED display, each pixel also has an LED which will discharge the capacitor between frames, leading to the flickering.  A good solution might be just to double the frame rate so that the flickering is at a higher frequency and therefore less noticeable.