I agree that the popular vote is a key metric, extremely important, perhaps even more than maintaining a close relationship between those elected and the voters

I agree that the popular vote is a key metric, extremely important, perhaps even more than maintaining a close relationship between those elected and the voters, which is often the goal of the balancing rules. As for an example, look at Germany before 2011 or Britain even now. (If you're not familiar with Germany, it used to allocate about half of the Bundestag seats in a manner like the British, and the Bundestag elects the government. In 2011 the system was modified to keep the distorting effects small. I glanced at a random wikipedia page now, for 1994, and the winning coalition got 47.5% of the votes and 51.1% of the seats.)