It's a problem when you're dealing with decentralized systems (read: Byzantines general probelm). If there's no central authority, how do you verify the person actually has the money and isn't lying / double spending?

Bitcoin is an example. A wallet is unique data (private key) that is stored only the users storage. That private key proves ownership of funds owned by a wallet address / hash. A wallet address has funds if someone with valid funds sent money to it. A person initially gets that data by mining, which is like spending computational power to solve a puzzle, in which solving also processes a set of transactions at the same time. This is like the process of minting, except anyone is allowed to mint. It also helps identify who the miners/minters are, since utilizing energy gives a signature (It's really hard to hide using a megawatt of energy with a thousand computers, for example)

A use case is it allows people in war torn countries to consolidate their wealth digitally. Gold, for example, could easily be confiscated at the border, or the refugees currency could only have value in their country. Lebanese people had their money squandered by the banks and the government, because they were the central authority. In a system managed by people, over a long enough period of time, a bad actor will gain some control of the system. This effect is worse the more control is centralized.

It also means you couldn't sanction other countries the way the America is doing to Russia's banking system right now. I'm indifferent about that argument but maybe you think those sanctions are good in which case would be a point against decentralized currencies.

I think more interesting ideas in blockchain involve decentralizing ID. A microchip in the heart can both act like a smart watch by monitoring health data and represent a unique identity in a decentralized system by using the biometric information like a fingerprint scanner. With a secure decentralized way to establish identity, you can decentralize voting, and remove politicians from the political system