Let's consider exactly what could make someone leave, as you've mentioned chemical spills, nuclear accident, rioting and yet despite recent events ignore the weather. I guess you don't live in hurricane country. But even failing that a big enough earthquake, and they can happen anywhere, history of quakes or no. (The great Missouri quake is estimated to have killed a million people, was felt in Boston.)
The whole point of having a bug out gun is as a part, an important part, but just a part of a bug out plan. We plan for likely eventualities, however remote and then old fickle fate steps in and throws something completely unexpected at you.
So, something unexpected happens. You have to make the decision to bug out or bug in. Adding up the factors in your decision you decide to bug out. So do most of your neighbors. Most of your unprepared neighbors. You are sitting in an endless traffic jam for hours and hours. People may be hot, running air conditioning to keep cool and using up their gasoline. They feel they've got to leave everything behind and go. After hours and hours they're out of gas. You're prepared, you've got gas. Assuming somebody else has a gun and they want your gas, how do you plan on keeping it?
Or you've decided to bug in. As Katrina shows, a depopulated city with minimal law enforcement still suffering from disruption of essential services is ripe pickings for vandals and looters. Maybe you've got a generator, or food, or for that matter drinkable water. How do you plan on keeping it?
And again, Katrina showed us that once you enter a shelter you are no longer captain of your own destiny. The gummint has you in their clutches, may not let you leave and certainly doesn't want to let you do anything to improve your condition.
No, they'll be playing hockey on the river Styx before I go into a shelter.
For that matter why are we talking about A bugout gun? If you feel the need to carry a longarm a sidearm is reasonable for most people. Not to say I'm lusting to bust caps at some bad guys real or imaginary. A modest display of firepower may convince the goblins that there are easier pickings elsewhere.