Many Western countries draw their governmental systems from the ideas first conceived by the Greeks and Romans. Democracy, equal representation, etc. all were first born in those societies. Thus, governmental architecture is often a tip-of-the-hat to those societies.
Also, the Greek style of architecture (and the Roman style that was, perhaps, one of the first instances of plagiarism) relied on perfection. This is just one example of the society’s fascination with perfection. Angles, perspective, etc. were all designed to be perfect in the eyes of the beholder. Governments often strive for this same perfection.