...and I realized that it's a lot easier to make an LCD or a plasma display do digital than it is to get a CRT to display digital.
Everything about a CRT is analog, from the way the display is refreshed to even the brightness of the pixels. An electron gun is hard to turn on and off quickly; over the past hundred years or so we've gotten quite good at it, but an individual pixel on a CRT is still a fuzzy, round dot rather than a nice sharp point. (At some point, Heisenberg's Uncertainty Principle comes into play, too, you know.)
But with a flat panel, all you need to do is route the correct bits to the right pixels (suitably adjusted for voltage and current, of course). There are no convergence adjustments required (or even possible) with LCDs; the pixels either line up, or they don't, and if they don't the panel is scrapped before it leaves the factory.
I don't doubt that we'll still have uses for the old glass bulb displays; steering electron beams around isn't going to disappear quite yet--but I think their days are numbered.