Does that make his criticisms of democracy any less valid?
1. If democracy is bad, we should have some other system. Surely we should take into account the proposed alternative when we consider any criticism of democracy itself.
2. Implicitly any reference to the writings of Plato is burnished by the image of "wisdom of the ancients," so it is worth considering the flaws of these philosophers' work.
The Greeks were certainly wise, but my main point is this is not untrod ground, we've got at least 2000 years of experience to draw from.