It's also a great example of politicians choosing their voters. If we are going for this system, why not just do a state-wide popular vote election and choose the top N people as winners?
Also, gerrymandering seems responsible for the candidates sliding further into extremism. Basically if you run in a freshly created district that you are reasonably sure will go to your party, your real competition isn't the Dem/Rep who is running against you. It's your opponents in the primary. So if you are a Democrat running against a Republican in a close to 50/50 split, you might be compelled to become more centrist to steal some votes. But if you are only concerned about the primaries, you will try to be the Democratiest Democrat ever.