Who gets to ask?
In the Stack Exchange (SE) system, the person asking determines the accepted answer. That's not a big problem if one person is the clear beneficiary. But what about systems where multiple people benefit? Who asks would determine who gets to accept an answer.
Subject to corruption
There are regular concerns about people banding together with friends to influence the system in Stack Exchange. This hardly ever happens. Why not? Mostly because the results of being the highest voted or accepted answer don't matter much. If your answer is accepted over mine, it may bruise my ego, but it doesn't actually matter. I don't make less money or have to do more work as a result.
In your system, the outcome would matter. As a result, all those worries about people banding together to control the outcome become justified. Tactical voting would become rampant. Closing questions so that you can ask your own question and control the acceptance criteria would be useful.
Who's the dictator?
Many aspects of Stack Exchange are controlled democratically. But in the end, the Stack Exchange system is a dictatorship, not a democracy. Stack Exchange can reverse votes (e.g. if you go around down-voting a single person for disagreeing with you) and delete questions and answers (e.g. spam).
This works for Stack Exchange for two reasons. First, they are a relatively benevolent, hands-off dictator. We rarely feel the tyranny because they are careful about using it. Second, because Stack Exchange is optional. If I decide that they are abusing their power, I can start a new site called Queue Swap tomorrow that does the same thing. If most people agree with me about the abuse of power, I'm likely to get lots of people joining me. That possibility keeps them honest.
Your system would not be optional. So we'd have to have some way of controlling the "dictator" in the system. But in the end, that just gets us back to something mostly like the current system. An empowered executive who can make the real decisions. A frustrated minority grumbling under those decisions with which they disagree.
Who determines urgency?
every important decision is taken based firstly on its ranked urgency
Who determines whether a decision is important or urgent? This isn't unsolvable, but the Stack Exchange system does not generally solve it. Meta decisions tend to be non-binding, although some people will choose to follow them. The real decisions about the importance and urgency of changes on Stack Exchange tend to be made by the benevolent dictator.
What happens if the dictator disagrees with you? For example, Obama finds Zika to be important and finds terrorism to be less important.
Free markets as Stack Exchange
Note that a free market economy gives many of the same results as you are trying to get from your Stack Exchange system. Most decisions are made by individuals. Multiple answers (products) can receive up-votes (purchases). Your individual decision controls your personal environment, much the way that acceptance controls your question in Stack Exchange. High reputation (wealthy) users have additional moderation powers. Yet you don't seem satisfied with this system and want to change it.
As you may gather, I don't favor this change. That said, the question of how to make change is certainly answerable. You need to find supporters and take control of the mechanism for making changes in your country.
To use the United States as an example, this would require either two-thirds of Congress or sufficient support in state legislatures to call a constitutional convention. If a convention, you'd have to make sure that they voted for your amendment. Then you need to ratify the amendment with the approval votes of the legislatures in three-quarters of the states (thirty-eight or more). Note that the last time we had a constitutional convention, we ended up with a new constitution instead of simply amending the old one.
This is the age old method for making changes. It's not fast. In the US, Republicans as a party were in favor of women's suffrage in 1860 but did not actually pass it until 1920.