> you lose the concept of independent components
How? Components take props. They're just as independent as they were previously.
> everybody is notified of the inner state of each component
This... isn't the case.
Redux (and Flux in general) is useful when there is application-level data that needs to be shared across different components, and otherwise something ends up being a prop to a bunch of things that shouldn't be. Or when you want something to remain around when components go out of scope. If you don't have this problem, Redux is overkill. For larger apps, it's damn useful.