No it did not. I don't know why people repeat this so often but it is very frustrating. Nixon unilaterally ended the gold standard because the US was printing money to pay for Vietnam and the rest of the world called the US on its bullshit. The end of the gold standard is relatively recent in history and the verdict is still out on the impact.
I think your observation assumes that inflating the value of gold relative to the rest of economy is a problem - if you do not care about that I'm not sure it matters.
In any case gold served as a strong check on monetary policy even if it had problems. Certainly it is possible to have a "sound" monetary policy without gold. I'm just not convinced in societies ability to affect sound governance of monetary policy without some "stronger" guard rails. Especially not in today's climate.