Pardon my GenZ analogy:
Like YouTube, you would end up with superstar representatives that would capture an even larger share than the most powerful do now. And the fact that they wouldn't even have a home district would mean that they would be accountable to absolutely no-one besides those who helped them achieve their superstar status. So yes, you would have "your rep" but he would be like a small you-tuber compared to PewDiePie—4k subs vs. 100,000,000.