modern militaries have leaps and bounds better weapons than anything civilians could possess.
That's true. I would say that in Vietnam, Afghanistan, and Iraq, our soldiers had "leaps and bounds" better weapons than anything their enemies did possess. However, the enemies still managed to hurt and kill our soldiers.
Air power, armored vehicles, missiles... there are all kinds of overwhelming weapons that civilians are not going to have that the military has. And if the military ever used those on the civilians, all the civilians could do would be to get under cover or go somewhere else. But it's impossible to use those sorts of weapons as an "occupying" force, and the more-lightly-armed civilians would inflict losses on the occupying soldiers.
even worse, this operates on the premise that the only way to have civilization is through constant fear of one another.
There is an old saying: "If you would have peace, prepare for war."
It shouldn't be necessary to live in "constant fear" but equally it should be possible to be prepared for the worst case.
I'm going to turn your statement around: you would have us arrange things so that if the government ever did go off the rails, the civilians would know that there was absolutely nothing they could do about it. Is that really better?
Governments can do things wholesale, and when government starts killing people, it does so wholesale. Nazi Germany got really organized about killing Jews... and I don't believe that the German people were innately evil or really completely unlike the people in my own country. Likewise, under Stalin, the Soviet Union got really organized about "purging" people; and look up "the killing fields" in Cambodia sometime. These events are history. They happened. It's not impossible for such things to happen again, and if you want to claim "it can't happen here" you had better explain why.
My answer: it can't happen here because armed citizens would fight the government, and would have effective weapons with which to do it.
The top two rights in the Bill of Rights: freedom of speech, and the right to own and carry effective weapons. These were intended by the authors of the Bill of Rights to be checks on government power.
Nobody wants to see the citizens of our country needing to use firearms to fight our own government. But the fact that they could, if necessary, makes it less likely that they ever will need to do so.