I've never seen a display with a 24Hz refresh rate. You know enough about monitors to realize that LCDs have a minimum refresh rate of 60 Hz and that a flicker-free CRT, such as the Sony Multiscan G400 that I'm using as I write this, needs a minimum refresh rate of 70Hz otherwise it's a strain on the eyes. What's the matter with you?
Right back at you. A CRT has to have a high refresh rate because the phosphors in the tube emit a very short burst of light as the electron beam strikes them, and then quickly fade back to black. Any given pixel on the screen is lit less much less than 100% of the time. If you use a fast shutter speed to photograph a CRT screen (1/120 or faster) you will see a horizontal black band on the screen that follows in the wake of the beam--at any given instant, a large portion of the screen is completely dark. As a result, a CRT monitor requires a high vertical scan rate (>60 Hz) for our eyes to blend the flashing pixels into a smooth continuous image.
In contrast, one of the engineering challenges of designing LCD displays has been to make a pixel that can react fast enough to meaningfully display higher frame rates. Unlike a CRT, an LCD pixel does not fade to black between scans--it continuously displays a color until the next frame arrives, and then it fades fairly smoothly from the old color value to the new one. How long this process takes is defined by the response time of the LCD. The response time of the LCD also limits the maximum frame rate the LCD can display. A high-speed photograph of an LCD display will not show any black band in the image the way a CRT will. Each pixel is illuminated 100% of the time.
A true 24p HDTV may overscan at some multiple of 24 Hz (probably 120 Hz, since that divides evenly into both 24 and 30 Hz) to reduce the transition time from one frame to the next, but that has nothing to do with the high refresh rate needed by a CRT. While a CRT scanning at 120 Hz is flashing each 24p frame 5 times, a 24p LCD simply displays each frame for approximately 1/24th of a second. The LCD is not "flashing each frame multiple times" even if its internal scan rate is a multiple of 24 Hz. Each displayed frame smoothly fades to the next frame over a time interval determined by the response time of the LCD and its internal scan rate.
Here's an experiment for you to try:
Go to an electronics store that has a variety of plasma, CRT, and LCD displays--monitors, TV's, and HDTVs. Bring a DSLR with a fast lens. With the shutter speed at 1/1000 or faster, max ISO, and the lens wide open, photograph as many different displays as you can. Have the camera in portrait orientation so that the shutter curtains are traveling 90 degrees to refresh of the screen image. Make a note of which displays exhibit banding in the captured images, and see if there is any correlation to the perception of smoothness or flicker in the displayed video. Post your results.