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Is it to do with the phosphor coating on the inside of the tube face that causes this or is it the fact that it takes a while for the EHT voltage in a TV to "die down" after intial turn-off?.
Anyone with knowledge of the old B&W sets would be familiar with the centralised dot in the middle of the screen.

The dot in the center of the screen was there for a short time while (a) the EHT voltage leaked away and (b) the cathode of the electron gun cooled to the point at which it would stop emitting electrons. This took much longer than the time needed for the vertical and horizontal scanning fields to disappear, hence just the dot and not a full raster.

Many manufacturers actually added a section on the on/off switch (or used some other similar method) to bias the tube into cut-off to prevent the dot.

The overall faint glow right across the tube face you can see in a darkened room after it's switched off is the persistence of the phosphor. I remember doing that with "Test Card F" as a kid! Turn off all the lights, then switch off the set and see how long I could still make out Carol & her companion! [Linked Image]