The power of military weapons is great if you want to bomb buildings and burn down bridges, but there is no point fighting your own people just be crowned King of the ashes.
Estimates for counterinsurgency are that an occupier needs ~20 soldiers for 1000 occupied civilians. The US army has 1.3M troops - the entire might of the US military would be needed to pacify just CA alone, and that would leave the rest of the country virtually defenseless. It's easy to bomb a building from a jet; it's much harder to kick in doors and arrest dissidents _even if_ there is no armed resistance.
The hard truth that allows democracy to survive is that it is not possible to govern without the consent of the governed. It is certainly not possible to occupy a rich, productive region and have it remain rich and productive unless the occupier has overwhelming force.