I don’t think ideological self-identification polls tells us much about policy views, but I think it does tell you a lot about things like hippie-punching and preemptive compromising:
People who think of themselves as “conservative” are in a very real sense the “base” of the Republican Party. A politician who positions himself as to the right of Susan Collins but the left of Jim Jordan is doing what most self-identified Republicans want. But “very liberal” Democrats are a marginal block of people, and the median self-identified Democrat also self-identifies as a moderate. Liberals just aren’t the “base” of the Democratic Party in the same way that conservatives are the base of the GOP. Balanced news coverage is all well and good, but commitment to balance sometimes distracts people from the fact that the parties are very asymmetrical in their structure and composition.