But surely the gold-owner would have to cash out some of their gold to pay the guard in cash? Does it make a difference if he pays the guard in gold and then lets the guard cash it out?
The gold storage cost is the equivalent of buying a cold wallet and keeping it in a safe place (crypto has that as well, but it's not a problem). The 'mining' is the equivalent of subsidising a banking system
The Protection Department would not last long against a nation-state attack. In contrast, BTC has no nation-state or military protection.
If people decided that gold was not valuable as money, it would retain at least some value based on its usefulness alone.
[0] Ok, I guess you can burn paper money or use it as a chair, I think Weimar hyperinflation had examples of that…