The role of citizens in creating public policy varies depending on the system of government, the nature of the citizens, and the type of policy. Setting, for example, interest rates in Saudi Arabia, public health policies in China, or environmental policies in the United States are all very different things.
In direct democracies, citizens are expected to vote on all major areas of public policy. In republics, in theory, they elect representatives who vote for them on policy, but in more autocratic regimes, people may have little say on policy. All of these systems of government have existed for over two millennia, and seem to function reasonably well.
The next issue has to do with expertise. Although in principle it seems fair to let all citizens have a say in public policy, in actual practice there should be some minimal degree of competence required. For example, one would not want people who do not understand global climate change influencing environmental policy or medically ignorant members of the anti-vaccination movement making choices which affect people's health.