There are a variety of reasons it would be an ideal material for a mirror but one that has not been mentioned is it's thermal properties and homogeneity. Polymers are very sensitive to temperature differences, PMMA has a coefficient of thermal expansion that is about 20 times that of Pyrex, a small change in temperature results in large changes in dimensions. This in combination with the difficulty in making the material exactly uniform throughout the sheet would mean the mirror would not maintain it's shape.
Other issues mentioned at the stiffness and hardness, PMMA is about 1/20th the stiffness of Pyrex and something like half the density, that means a comparable thickness piece would deflect about 10 times as much under gravitational loads.
PMMA works for small, non critical optics but for telescope mirrors where fractions of a wavelength of light are critical, I wouldn't recommend it.