From online reading and my personal observations, CRTs have lower phosphor persistence than LCDs, resulting in both the flicker and clearer motion. I think interlacing works more due to persistence of vision, and because the beam is thick enough to nearly fill the scanline gaps. You can actually simulate interlacing on a LCD by showing simulated scanlines, alternating by half a line each field/frame. There's a video demonstration at https://youtu.be/tS0cFwvDWkE?t=480.