When you’re in a “siege” situation, it really comes down to what your ultimate goal is. If you’re trying to apprehend whoever is holed up in their shack with an AR, obviously you’re not going to light the place up like an Old Western and sort through the ashes. The reason most of these things take so long is that it is never the intention to just straight up murder everyone inside, therefore a couple of nuts with automatic weaponry can “hold off” the police for however long they feel the need to hang around. More often than not, there’s also the question of innocents and third parties lumped in with the gun nuts, so you can’t really take immediate, aggressive action like sending in a SWAT team.
So yes, effectively anyone with a gun can hold off an assault, simply by virtue of people not wanting to risk personal losses over one idiot with an assault rifle. Much like actual military sieges throughout history, it’s usually just easier to wait it out. People inside can’t get more supplies or change their situation, while those doing the seiging can wait around til the end of time while Jim Bob runs out of bullets and food.