If you compare it with a basket of goods it's still highly unstable. It's not a true random walk, but day to day gold fluctuations can be extreme and it's still in the middle of a bubble so expect a sudden crash some time soon.
With a gold price that high, it might become profitable to just synthesize gold in a nuclear reactor. Which would destroy the point of imposing a gold standard in the first place. Even if it wouldn't be profitable with today's technology, it would become a very lucrative field. Which you would have to outlaw. Etc. etc. etc.
What all the gold nerds are really clamoring for is an international agreement saying that no one will ever increase the money supply. This won't happen. A system of fixed currencies is as unrealistic as every nation suddenly deciding to adopt communism.
It would be an interesting mathematical exercise to define a cryptocash-like token that could be subdivided indefinitely without being duplicated--you could use this token as the basis of a permanently fixed money supply. Not sure how useful that would be in real life, though.
There have been centuries when gold was legal tender and nobody complained (apart from some emperors who found debasing gold coins by adding copper was a bit difficult; but printing press has not been invented yet).
So when you compare 2 things one of whose value is stable like USD or a basket of goods, and something else that is unstable like Gold. Then the unstable item makes the value of the other things seem to fluctuate. However, by making several comparisons you can determine that the ratio of USD to basket of goods is stable but gold vs USD or Basket is unstable so it's Gold that is unstable.