If you have a totally disengaged population, it greatly impedes the ability of the government to get anything done.
That's the real genius behind democratic forms of government. It's not that noise about "freedom" or whatever, it's the promise of a real stake (however small) in the nation. That stake gives people a real reason to participate, to buy in to the whole thing. Any practical discussion of "Responsibility" is really dealing with that engagement issue.
Throughout most of human history, most large government has oscillated between coercion and benign neglect. Things like tax evasion or other forms of avoidance were generally far more accepted and approved of.
But the nations with the best outcomes were usually the ones that best maximized the engagement of their citizens. The more engaged people are, the less waste you have and the better you'll do with the resources and circumstances available. That's a big part of why the British beat the French in the long run in Europe. The French had great demographics (way better land and a lot more of it, way more money, and a significantly higher population) but it was the English with the more engaged population. The only time the French really properly used all their resources was the one period of time the French population was really collectively on board with the government.
That's where national health insurance and welfare and such come in. You're maximizing the utility of your population. On a psychological level people feel like they're being protected and supported and on a practical level you're maximizing the health and well-being of your population. Enlightened self-interest and all that. The future challenge I think will be for a nation to affordably find ways of engaging people who are more and more marginal, such as people with serious mental or health issues.
Anyway, rambling diatribes aside, the point being that Democracies tilt people towards engagement with the government, but that this is not something that ONLY occurs in democracies and is not necessarily an inherent property of any particular government type.
I'm not really arguing your philosophical idea of what government is theoretically for (I probably agree that part of the government's function is exactly what you describe - arbiter of the social agreement), more the practical outcomes. And a good practical outcome does require good leaders, but it also requires good people. It's a positive feedback loop.