"We didn't have enough to honor the obligation."
True, but not the full story. We've never had enough gold to redeem all of the outstanding dollars. The value of the dollar does not derive from gold. It derives from trust.
By the time Nixon became President in 1969, we had not been backing the dollar with gold for more than 35 years. One of the first things Roosevelt did after he became President was push thru a law that said we would not honor our promise to exchange gold for gold certificates. He even banned private US citizens from owning gold altogether. It went up to the Supreme Court, and the Supreme Court agreed that the law was Constitutional.
So it was Roosevelt who ended the connection to gold, not Nixon. And after Roosevelt ended the connection to gold, was there a deluge of rampant inflation? Absolutely not. We were in fact in the middle of one of the most extended periods of deflation in history: The Great Depression.
So we were not even on the gold standard at the time Nixon became President. Rather, what Nixon did was abrogate the Bretton Woods Accord, which said among other things that the dollar had to trade in a certain range, vis a vis other currencies, and that the US Treasury was required to intervene to make sure that it did.
When it did intervene, however, it did not do so with gold. What it did was intervene in the financial markets. The reason Nixon was forced to abandon the Accord was that the monetary pressures were simply so great that he'd have had to cause another depression in order to maintain the US obligations under the Bretton Woods Accord, and he wasn't willing to do that.
I'd have to say that it may be the one and only thing that Nixon did correctly during his Presidency. I think that virtually every economist would agree that it was the right move, regardless of political affiliation.
The value of the dollar derives from trust? Trust in what, how? That is an incomplete statement. It is unipolar and makes no sense, it is yin without yang, plus without minus. Trust does not stand alone, it requires a partner, it must be trust in another to do something or not to do something, to fulfill a promise. I suggest that the value of the dollar back then derived from the trust that precious metal coin was backing the paper at a ratio of 1 to 1, and that redemption on demand would be honored. In other words, they trusted that they could get their gold. Therefore the value of the dollar paper derived from the gold. People knew they were trading title warehouse receipts for gold and or silver. People often ran on the bank to get out the metals when they felt the government was not backing sufficiently, the system was self balancing. If you had told one of them that the value of the dollar derives not from the gold, they would have laughed. Even our dollar today, trust does not enter into the equation, we accept dollars because we believe and hope someone else will accept them when we go to spend them, and they are receivable for taxes. Often we don't even question that others will accept them; but we understand and expect others to raise their prices which is in a way like conditionally not accepting them...at the old price, that when they lose their value to inflation, the merchants say I won't accept them at the old price but I'll accept them at the new price, which means you pay more.