CCW just means you're more likely to be armed if TSHTF when you happen to be on the street. In most "shall issue" states, that means that in any crowd of thirty, there will likely be one or two CCWs.
Within an hour of TSHTF, you will have 150 million gun owners at DEFCON 1.
In a big event, which could last days, weeks, months or years, your paper license in your pocket is absolutely meaningless.