1) Gold is NOT remarkably stable, just look at a 40 year chart. No one cares what price gold was 5,000 years ago or what price it will be in will be in another 5,000 years.
2) A gold backed currency or (relatively) fixed supply of money does NOT bring economic stability. There were far bigger booms and busts on the gold standard than off it; ever hear of the Great Depression? Or look at what has happened with Bitcoin, a currency invented designed specifically to stop banks debasing currency - $0.01 to $20,000 and back to $4,000 in 10 years.
3) The modern world will never go back to using 1,000 year old technology like gold. If fiat currency is ever replaced with a fixed supply currency it will be a crypto currency with block-chain technology.