Arguably the dollar price of gold reflects the dollar's instability. You see run-ups in the dollar price of gold after the inflation / stagflation of the seventies and with whatever the Fed has been doing the last few years.
The problem I see is that fears of inflation swing much more wildly than actual inflation. If the gold price were a reflection of actual dollar instability, a chart of the inflation adjusted gold price should be a flat line. In fact it shows swings of several hundered percent.
The price of gold is a reflection of inflation fears, not of inflation. I'm not saying it is too high or too low right now. But gold is clearly unfit for purpose if you're looking for a safe haven or a store of value.
I would argue that it is, the flat line could be said to have tripled from the seventies to right before it took off during the current panic. If one had bought gold before the panic and held long they would most likely see the same trend as was seen from the 70's up until the panic. The thing about gold is it is subject to panic buying when currencies are debased and it is exactly the time that someone that has held long in gold should vacate there position, wait for it to implode and then double down on it again. Gold purchased at it's baseline is actually one of the best hedges available. The problem is gold goes unnoticed until there is a panic. Institutional investors ignore it because it's performance is long while others ignore it because it is not a high profile security that the institutions are chasing.
It's not just inflation, though. Compare the history of platinum prices with those of gold. There is definitely a psychological component to the run-ups in gold which has nothing to do with immediate economic pressures.