I resisted for a long time, but finally switched from a callback model to Mobx and the reason was that ShouldComponentUpdate and ComponentDidUpdate started becoming unbearably hard to manage.
So state management libraries are not solving a unsolvable problem, they are here so that we can write cleaner, more efficient code that potentially can become more performant. At least that's what happened in my case.
Can't you use pure components as long as you make sure that all your callbacks are called with new objects, e.g. using the JavaScript spread notation?
I think the bigger reason that a global state management system becomes necessary is when the shape of your component tree doesn't closely match the shape of your state tree, because that means state (and callbacks) need to be passed down through components that don't care at all about that state simply because one of their distant descendant components does care about it.
So state management libraries are not solving a unsolvable problem, they are here so that we can write cleaner, more efficient code that potentially can become more performant. At least that's what happened in my case.