Why does static electricity not make a charged body reflective?

From the wiki article on the coulomb

Since the charge of one electron is known to be about 1.60217657×10^−19 coulombs, a coulomb can also be considered to be the charge of roughly 6.241509324×10^18 electrons.

Reflection from metals, usual substrate of mirrors, involves the fermi level electrons of the material. Silver with $5.5\,$eV fermi level will have $5.9\cdot10^{29}\frac{1}{m^3}$ free electron density so even a coulomb in numbers does not add that much extra electrons in comparison. I suspect that is why extra charge would not make for measurably better reflectivity

Glass does not have free electrons to start with. It's an insulator. If you add some electrons these won't be free electrons either. They will be localized on some negative ions. The reflection from insulators have nothing to do with free electrons. So your question is based on a flawed premise.