I suppose that's a viable approach, but I'm genuinely curious: if you're going to go to that route, why _not_ use Redux? Besides, the wrapper components generated by the React-Redux `connect()` function help serve that purpose of encapsulating store subscription and interaction, and keeping your real components agnostic of where the data is coming from.
The simplest reason? One less thing to learn. Once you get a feel for things you can pull in redux, but people already have a kinda hard time getting setup.