Buddy, Can You Spare A Dollar?

You can hoard all the paper currency you want and insist on using it everywhere you go. The problem is, our global economy is already digital and that paper (polymer) money in your hand is only worthwhile if someone else wants it.
 
If the economy collapses to a state of deep recession or deep depression paper (and digital) currency will mean nothing.
 
Even if the paper currency were to retain its' value, which it won't, inflation will skyrocket. What you could buy with that $5 bill today won't even be a downpayment on the item tomorrow.
All you are doing by drawing money out of the banks is to scare the elitists who control the banks. This will lead to protectionist measures to keep a firm hold of your money from you. Higher interest rates, more service charges, lower withdrawal limits and so on.
 
In an apocalypse, two things have value - practical material goods (assuring the basics food, shelter, and clothing) and personal skills (your value in the collective or on your own). Paper currency will be worthless.
 
Anyone who says people will still take currency seems to forget that the government determines what is and is not legal tender. Remember the penny? Poof. Gone. They can just as easily do that to physical currency if they want to.