For this to be true, you need a majority of the population to be well informed voters, which just isn't true. I'd be surprised if 25% of American's knew about a US bomb blowing up a bus of schoolchildren recently, and doubt a strong majority would support that bombing. Yet my vote does not matter on the issue.
Not saying it's a bad idea. Questioning whether you're contradicting yourself.
Not really, even on some highly salient issues. Universal public health care has had majority public support most of the time since the early 1990s, but the Democratic Party has opposed it (in favor of various complex public/private schemes with insurance companies front and center) as has the Republican Party.
It's even less true in issues that are of extreme interest to a narrow group and low public salience.