I wonder why we use something polynomial-based instead of something exponential-based like the decibel scale?

A power function seamlessly maps 0 to 0 and 1 to 1, easy for black to white.

An exponential/log function requires arbitrary clamping or offsets because you cannot represent pure black, 0, on a pure log scale without hitting negative infinity.

Basically, it fits better, aside from a good map of human perception