I'm not sure what "US gun culture has to do with the dissatisfaction people have with their system of governance and feelings of powerlessness", or that it matters.

Near as I can tell you have: a) people who believe they should exercise their rights in order to not lose them, b) people who believe having a gun or three will better help them if ever they are burgled while at home, c) people who believe that an armed society is a polite society, d) people who believe that an armed society is less likely to become tyrannical, e) preppers, f) hunters/sportspeople... These groups/motivations often overlap. You only need one of these motivations to convince you to own a firearm, but many people will be swayed by just one of these. It seems every week we see a news item about a burglar repulsed by an armed homeowner, for example. And recall that the plaintiffs in Heller (the case that established that there really is a second amendment right to have firearms) were gay people in D.C. who felt unsafe. And recall that during the Civil Rights era (and before! going back all the way to Reconstruction) many black people felt they needed to be armed to resist lynchings (were they wrong?).

I didn't list "dissatisfaction people have with their system of governance and feelings of powerlessness" because, as far as I can see, that's not a common reason for people arming themselves. Fear of tyrannical government is one reason people arm themselves, but I wouldn't say that's a feeling of powerlessness, or of dissatisfaction with government -- it's not at all incompatible with feeling empowered and satisfied with one's government.

It is true though, I think, that if push came to shove, the fact that people are armed wouldn't be likely to make much difference to a determined tyrannical government that can mobilize (and motivate) modern military and/or police forces against rebels. But it sure would be easier for a tyrannical government to have a disarmed population. It's not for nothing that tyrants generally disarm their populations (Hitler, for example, did this). Thus having a well-armed population functions as a canary in the coal mine: if and when the would-be tyrants decide to confiscate firearms, that's when you might start thinking about hopping on a plane to some other place for a while. As a corollary, if the U.S. (federal and/or state) governments don't go confiscating peoples' guns, many people will not think them tyrannical.

For me, as long as we have free, orderly, timely, and clean elections, and as long as the state espionage machinery is not used to twist elected officials' arms, then we do not have a tyranny that cannot be corrected at the next election day. One of the most enduring parts of the American Constitution is that it focuses on process and that those constitutional provisions establishing process are the ones that have least been ignored, maligned, or violated by the institutions it provides for -- the U.S. Constitution is a work of genius, and this multi-century resiliency (while also being flexible enough to be amended, and with a Supreme Court that has enough power to fill in the blanks) is something to behold.

The Constitution is ultimately the biggest reason that the American system is stable, not that the people are armed, but I'm not at all convinced that the people being armed has no role in this, for there is another reason for American stability: its great decentralization and large geographic area. How would one mount a coup in the U.S.? I don't see how. In many countries you see the military (say) take over TV and radio stations, newspapers, shut down the Internet or otherwise impose severe controls on it, and park tanks at key intersections in key cities, and then it's all over. But in the U.S., if someone tried this, they might control one, or maybe two cities, but the rest of the country could easily refuse to go along -- how would one make sure 50 states go along when they all have national guard units, and some even separate militaries as well? It would require a civil war, and no one in the U.S. wants a civil war. In a civil war, the fact that so many civilians are armed would definitely count for something, thus making a coup even less likely.

IMO.