Fiat money was designed to be centralized and handled with the help of financial institutions such as banks, which usually collected their instructions from higher authorities like the government. Because of how they chose to run the (our) monetary system, you cannot say that such money is un-sound.
Exactly, and as a matter of fact, we need to always understand that both the centralized system of money and the decentralized monetary system serve different purposes and one cannot rule out the other because, at the end of the day, people would have reasons to why they should keep using one or the other.
The decentralized monetary system is that which you can use within your purview and you can have a high level of control over it. Whereas a decentralized system is being managed by banks and, by extension, the government. Government today can decide to change the value of the money or even the currency type to something else and you have no choice than to follow.
But, at the same time, the government might be doing some of those things to retain the integrity of the currency. you can't say that the fiat currencies are unsound because you have chosen to go with a decentralized system. Governments are looking at how they can better their local currencies and that is why they will always work hard on their economy so that their currencies can gain value in the sights of other currencies across the globe.
When you are using a decentralized system, it's like a global and individual monetary system but when you are using a centralized system, it's between you and the government. So, the government can have a control over how the money would be valued by you and across the world.