You'd get a good sample, but a poor representative. If a group of people is attempting to choose a person to advocate their interests, they'll choose the person best at advocacy, who is likely atypical in a variety of ways.
Because typically people are bad at public speaking, rhetoric, bargaining, and other means of advocating their interests.
Not everyone has to address Congress. As long as each valid viewpoint has at least one advocate, I trust people could figure out the best option. Less bargaining means fewer riders and pork, which is a good thing. I'm fine if only the best ~10% of Congress wrote/debated laws and the rest simply voted.
Also, remember we are comparing against the current Congress, which only represents the wealthiest among us. Pretty low bar.
Because typically people are bad at public speaking, rhetoric, bargaining, and other means of advocating their interests.