* Intrinsic Brightness: White dwarfs are incredibly dense, but they are also very small and cool compared to main sequence stars. They are simply not intrinsically bright enough to be visible from Earth unless they are very close to us.
* Distance: The 100 brightest stars in our sky are mostly massive, luminous stars that are relatively close to us. White dwarfs, being faint, would need to be much closer than these bright stars to be visible.
* Evolution: White dwarfs are the end product of a star's life cycle. Most of the 100 brightest stars are still in their main sequence phase, burning hydrogen into helium in their cores. They are still quite young compared to the long lifespan of a white dwarf.
A Thought Experiment:
Imagine a white dwarf that is just as luminous as the Sun. For it to appear as bright as the Sun in our sky, it would need to be at the same distance from us as the Sun. However, white dwarfs are much smaller and cooler than the Sun, and they would need to be much closer than 1 AU to be that bright.
An Interesting Note:
While there are no white dwarfs in the top 100 brightest stars, there are some white dwarfs that are relatively close to Earth. Sirius B, the companion star to Sirius (the brightest star in our sky), is a white dwarf. However, it's so faint that it's difficult to see without a telescope.
