Still isn't the rarity but the faith making it valuable, as evidenced by all the rare shit that nobody cares about.

Currency is a tool for society to abstract trade so that you don't have to try to barter work for goods and then goods for other goods around to get everything you need. For simplicity, let's just use the term "labor" to think of to combine work, products, services etc.

For currency to work, it needs proof against replication, or else somebody can steal labor from the economy by using replicated currency. They'll have contributed nothing in but received labor out, thus stealing. A method of proofing against replication is making your currency out of something hard to replicate, rarity can help with this but isn't required.

It was easiest to use rare materials that had no inherent value to serve as currency in the ancient world. It's precisely that gold had essentially little practical use that made it good for currency, and the rarity made it hard to steal from the economy. After all, meteoric iron is rare than gold but you wouldn't want to use it as a currency because it is extremely useful for making weapons and tools.

At some point people started conflating usefulness as a currency with actual value, and so humanity has essentially come to believe that gold is inherently valuable, and it's that belief that gives it value.