> Except that isn't going to work, because governments are untrustworthy

Some governments are more trustworthy than others, and lots of people trust some governments. For example many people hold USD because they consider it a better store of value than their own country's currency.

> a trusted party could run a big relational database that was basically a non-inflating currency and really cheap to run

Somewhere like Switzerland would probably be quite trusted to run this.