[ordinary]

> It is the government responsibility, in their mandate as representatives, to address the problems perceived as important by the citizens

But it is the citizens' responsibility to make clear to their representatives the problems they consider important. For a couple of examples of this principle in action, see the civil rights movement of the '60s, or the marriage equality movement of the noughts and teens. No politician would've dared approach those issues until the citizenry made its voice heard.

As a rule, on issues that we as peoples consider important, we lead our politicians, they do not lead us. This is partly because of the incentives in play in modern democracies and partly because, as you say, they are merely our representatives, not our dear leaders.