The gold standard (and by extension fiat because it is still very similar to a gold standard because of the existence of cash) causes artificial wealth transfers from the poor to the rich.
Let's say you own 1% of the gold of the economy. Notice that you also end up owning 1% of the savings in the economy. If an enterprising individual increases productivity and his company produces more, the value of gold will go up, leading to unearned gains in the value of your savings. Since you own 1% of the economy and the gold standard artificially enforces this against the will of other participants, you will gain a 1% share in the improvements of the company even though you have contributed nothing and taken away potential income from the entrepreneur. If the invention caused the economy to grow by 1% then the entrepreneur would expect to receive a 0.9% in the economy. That share would require everyone to give up 0.9% of their savings. Meaning your savings must go down to 0.91% of the economy. Of course, this doesn't happen in a gold standard which massively hurts the productive economy and that is exactly why there is a constant need to mine out more gold, to let new entrants into the economy as the old ones don't want to give up their gold and let it circulate in the economy. The gold standard is effectively a tool for violence and extortion.
Even under a gold standard, savings don't have to be in gold.
We don't all carry our savings in fiat cash (or central bank reserves) today, either.
You can save in bank deposits (denominated in gold, or fiat money, or whatever your bank offers), you can save by buying stocks, you can save by buying a house, etc.
Let's say you own 1% of the gold of the economy. Notice that you also end up owning 1% of the savings in the economy. If an enterprising individual increases productivity and his company produces more, the value of gold will go up, leading to unearned gains in the value of your savings. Since you own 1% of the economy and the gold standard artificially enforces this against the will of other participants, you will gain a 1% share in the improvements of the company even though you have contributed nothing and taken away potential income from the entrepreneur. If the invention caused the economy to grow by 1% then the entrepreneur would expect to receive a 0.9% in the economy. That share would require everyone to give up 0.9% of their savings. Meaning your savings must go down to 0.91% of the economy. Of course, this doesn't happen in a gold standard which massively hurts the productive economy and that is exactly why there is a constant need to mine out more gold, to let new entrants into the economy as the old ones don't want to give up their gold and let it circulate in the economy. The gold standard is effectively a tool for violence and extortion.