The key difference is that there's an entire network that needs securing with a minimum cost to secure. By contrast you can secure your own gold for free by burying it in the ground if you so wish, and other people not securing it properly didn't prevent people from transacting with gold throughout history.

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

This is a very critical point!

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 owner would buy less gold, i.e. the gold they intended to buy minus the cost of securing it, but they don't have to sell gold. Buying less of something and selling an equivalent quantity of it is not equivalent.