To believe that lightly armed forces can’t defeat a government one has to believe that the Vietnamese lost and the Iraqis didn’t tie up the US Army for a decade.
Let’s start with the concept of an invader.
Said invader is likely at the long end of a supply chain. (Canada is not a likely invader, nor Mexico.)
Now, even if we accept the claim that very light infantry can’t do anything effective…it can be a screening force for the military members who can. Every veteran or trained hunter with a rifle acting as support, perimeter security, reconnaissance and facility guard is one more active duty troop freed up to engage.
And they are far more effective if they have commonality of ammo, magazines and parts with the regular forces. AR-15s don’t have quite the same internals as M-16s, but the pins, springs and accessories are interchangeable, as are ammunition and magazines. Suddenly, the US Army has a potential 30 MILLION more basic Riflemen.
But the claim they can’t do anything effective (beyond what we’ve shown) is false.
Rifle fire is just fine for harassment of troops in garrison, ongoing casualty infliction among support elements, and more importantly, their administration.
An invader, once amongst the populace, has limited options. If his goal is simply to destroy the nation, then there’s no reason to waste time within anything below strategic weapons. But what point does that serve?┬á And if that happens, with no subsequent invasion, then the utter chaos, collapse and starvation that will follow dictates that being heavily armed is among the top survival priorities.