Money is just information, like music. There is no reason it needs to be slow, expensive, or restricted - which all other money currently is.
Bitcoin is better at organizing the information of money than all other existing methods. This (+ scarcity) is what enables it to be valuable.
Specific bits in the bitcoin blockchain are not valuable, as you're stating. There are no individual bits in memory or on disk that have value. They're simply clones of the same distributed information, which is that you have some slice of the pie. It's your ownership of the slice of the pie that is valuable, because it is scarce, and because it is value-information that is fast, cheap, and global.
What does "backed by the full faith and credit of a stable entity" even mean? Why does it matter? Does it have anything to do with the organization of information? It seems like it doesn't.