The Specific Answer
The answer is "no solution." This question is based on false premises.
There are plenty of people who contribute to StackExchange who believe it is highly flawed. Many people disagree on what actions should be taken ("Is this on-topic or not?" "Should this be on this SE or that SE?" etc.) Many people take the "vote your conscience" thing to weird places that do not help the site. Sometimes whether your question is given "protected" status or "closed" depends on which band of high-rep users happens to be around at the time.
Many people who are active in cleaning up the site are more interested in whether your question or answer is technically on-topic than whether it is a good fit for the community or makes StackExchange better or worse. In fact, on some of the SE meta sites when people have asked questions about how to deal with certain types of actions, I have more than once included in my answers statements to the effect of "Ultimately, is your action going to make StackExchange a little bit better or a little bit worse overall? That is more important than a legalist interpretation of the rules." and had such answers yield a total negative score.
There is nothing "Utopian" about StackExchange. StackExchange's principles would no more bring about a physical utopia than they have a virtual one, since they haven't.
The Generic Answer
That addresses the body of your question. But the title, and some aspects of the body, also seem to be asking a more general question: If there were some utopian website that did exist, and if that website's principles were applied to physical, real-world governance, could the real state likewise be a utopia?
The answer to that question would be a bit different. Since we have no first-hand records of any people documenting any nation in a state of utopia, and I know of no large groups of people who even collectively agree about how to bring about a utopia, it is difficult to know. In fact, it might be impossible to answer this question: if we cannot even agree how to bring about a utopia at all, even in theory, then is it even possible to discuss how to transfer the principles from one medium to another? I'm not sure.
The "Anti-Utopia" Proof
I will tell you one thing that I do know though: if a utopia is perfection, all it takes is one person who believes that they are worse off to, by definition, make a situation non-utopian; so if you applied StackExchange's principles to my country's governing structure, I can tell you right now that there is near-zero possibility that any utopia could result since I would be miserable every time some group of 5 (or make it 500) "trusted" individuals voted to suppress what I was doing that day. You are going to get a lot of super-pissed-off people. Right now I live in a constitutional-republic with a semi-democratic election process (the U.S.), and it is already bad enough that my neighbors have so much control over my life - I would not want to give them even more control.
Thanks to discussion with @aslum for teasing out the following paragraph...
The problem here is with defining a utopia by terms of perfection. If we instead defined a utopia as just "a really good state where the average happiness per person is maximized," then things would be different and you might be able to accuse me of a "No true Scotsman" fallacy. As it stands, asserting "Everything is perfect" is easily disproven every time anyone complains (reasonably) about anything.
For this reason, it might well be literally impossible to have a complete and true utopia as long as it is defined as such, since all it takes is two people with mutually-exclusive desires to make the utopia impossible.
For example, I roll my eyes at "anti-gun" people, I believe that being allowed to open-carry firearms is necessary to a safe society, and I absolutely hate it that my state cracks down on firearms - I really don't care what anti-gun people think. For me, a utopia simply cannot ban open-carry of firearms. But I know that someone else might freak out every time they see me with a firearm, and they might (irrationally, in my opinion, but my opinion is irrelevant to this person) think I'm going to rob them; for this person, a utopia simply cannot include people open-carrying firearms. Our utopias are mutually exclusive. Therefore, if we use a definition wherein the neighborhood is perfect for both of us, our neighborhood utopia is not possible.