My point is, small arms aren't effective.

Ok, yes, I've seen that you've made this claim several times now. Do you have experience leading small units into battle? Do you have any direct experience with asymmetric warfare?

If the military isn't obedient.. ..an armed population isn't really necessary to actively fight the government.

And you think that a domestic insurgency would draw an all or nothing response from the military? If there were some kind of rebellion, it makes sense that it would start at the grass roots level. Furthermore, the entirety of the armed forces is not directly controlled by the federal government. The national guard is a state militia directly controlled and funded by state governments until mobilized by federal charter. It stands to reason that we would see active rebellion first within the ranks of the national guard before seeing it spread to federal forces.

They only need rise up and wait for the government to capitulate or to order the killing of civilians

And rising up would require the use of small arms..

which leads to a defection of the military and ultimately a coup.

Again, this is no all-or-nothing affair. Military rebellion would happen incrementally, most likely at the field-grade level, and would require attrition on both sides to gain any traction.

The idea that small arms are completely ineffective is totally laughable. Small scale operations, hit and run tactics, targeted attacks on key facilities, and support from the locals are key factors in winning battles and demoralizing opfor. These are also operations easily carried out by disciplined and experienced irregulars using small arms and home-made incendiary devices.