If that were the case, then you'd be right. But that situation doesn't exist and if we reach that point, then all confidence in the government -- and therefore its money -- will have been lost.
Paper dollars are intrinsically worthless. Their purchasing power is based on faith alone. I wish you luck hoarding your paper dollars. I really wish you'd sell them for some gold, though, instead.
Sorry, I know way too much about gold to want any appreciable amount. For me it is just a metal. As a thing of value it is far too hard to convert, so in many practical ways it is no more valuable than paper money.
For those who embrace it, though, I strongly recommend that they become learned about scrip, as it is one of the most effective ways to retain gold’s value and convertibility—not by being backed by gold, but by being a very controlled currency that is stable independent of gold. That is, it can make change for gold, and provide it access to the rest of the market.
Stability is the great secret of gold, but only backing something else. It has no great stability when it is used as a currency. The best demonstration of this was the transition, in Weimar Germany, from the hyperinflated fiat currency Papiermark, to the gold backed non-public currency, the Rentenmark, to finally the also gold backed Reichsmark, which even survived the war.
Gold itself could not have done that, but by backing currency, it could.
It’s not really necessary to horde cash, beyond a certain amount, but mattress money can be particularly good insurance against government perfidy.