Why do you consider “intrinsic value” for paper money but “trading value” for gold? What is the “intrinsic value” of gold?
Gold or paper money, all are used to replace faith/trust that we have to put in a 3rd party (govt) when exchanging goods (barter). You said that paper money is a promise in a bad sense but this is exactly what it is supposed to be. Unless you are trading goods for goods, you need a medium/bank/govt to ensure that they can promise to hold value of traded item (paper receipt of trade) and offer it to you later in exchange of something else that you want to trade. The key is how much trust you can put in the 3rd party. If the govt or 3rd party is corrupt, they will default on that promise and then it doesn’t matter whether they offered you a paper receipt in writing or a shiny metal in return. Abd we have seen historical examples from both sides.
The gold debate is about supply and demand, its about inflation vs deflation as monetary policy and its about trust. Sometimes gold bugs try to make it something different, calulating astronomical values of gold. The main advantage of gold is its limited supply chain and that historically it has been easily tradable. But for that matter, you can own Euros if you think European govt is better/honest than ours and Euros are more easily tradable, exchangable and storable than gold. The percentage of gold or land or food or Euros that you hold should be proportional to the probability you place on the defaulting of US govt. I keep it below 20% generally. However, investment/trading gold is seperate discussion.