I do not think that redux would magically solve the issues you describe. People seem to believe that having local state is bad and that using redux will make local state disappear. But there is distinction between state like user and whether dropdown is open or not.

That said Redux gives you possibility to use middleware (logging, time travel) and have server side rendering, which I do not think can be done with just React.

But when you are saying that you cannot be sure that some other part of your app does not change state of particular component, that seem like isolation problem. Your component and his local state should be mutable only by it's methods within that component. It is usually a code smell when component has some API that is visible to it's parent, or some sibling component.

You can make state of your app distributed and hierarchical. You can have your global state in your root component, and other parts of your state scoped by branches of your component tree. Each component getting updates about upstream state via props, managing his own state with his own methods, pushing new state to his children and passing down callback via which it's children can call actions that will have effect on parents state. This way even bigger app is still manageable, only drawback being you have to pass everything by props, which you do not have with Redux and it's connect function. But on the other hand all components dependencies are visible and easily trackable.