We know latinum cannot be replicated which gives it it's value in the Star Trek universe. But usually with metal based currency there is a productive use (Not historically, but presently and in the future). For instance today silver is useful for cameras and medical equipment. Does anyone know if latinum is actually useful in the production of anything?
Memory Alpha lists the known uses of Latinum. Note that all of them are vanity items:
Renewal scroll inscription pens
Waste extraction fixtures
- According to Nog, the waste extraction fixtures in the Nagal Residence are plated with latinum.
Additionally the "Divine Treasury" is said to be made out of solid Latinum. While it's a fictitious locale, its existence as pure Latinum also suggests its use purely for vanity.
Latinum is likely only valuable as it can not be replicated. Also note that the Ferengi are not a utilitarian species; money has inherent value to them, practical goods are only worth what they can be sold for.
A useless but impossible to replicate material is arguably the perfect currency for the Ferengi; it's the one thing you couldn't sell for more money. Ferengi obsession over what is basically pure money is likely commentary; one that would be lessened if they had practical reasons for their greed.