That is becoming less of a problem than it used to be. There are upscalers that can, with zero lag, take an RGB signal and output something over HDMI that a modern display can use. And there are certain displays (generally computer monitors) that can deliver sub-frame input lag with used with a good upscaler. It's not QUITE the same as playing on a CRT, but it's good enough for speedrunners of many retro games.
Such a setup isn't cheap, but it's far more reliable and space-efficient than a giant CRT.
Such a setup isn't cheap, but it's far more reliable and space-efficient than a giant CRT.