I think the reason fluorescent lightning looks bad is not the color temperature, it's the narrow spectrum of emitted light.
i.e. most of the light is UV, which is converted to other colors by phosphors - in precisely the same method LED uses. If it stopped there it would be great.
But it also makes visible light in narrow peaks, and this messes with the color, so they compensate by adjusting the phosphors for the complementary color, but that hurts the color rendering.
Bulbs at the end of their life can flicker, but those of course should be replaced.