That _is_ how I think about components, but it's still bananas. Render does not neatly describe this behavior because it necessitates setting unnecessary state. That's gross.
Usually when I need to trigger a redirect, I'm in some business-level function. So to redirect this way, I would need to set some state in my store, re-render, then hit the conditional, which would redirect, probably unset that state, and then probably trigger some additional business logic.
When really all I want to do is in the business function, directly trigger the redirect and maybe some other logic without any indirection. redux-react-router exists, but it's API is still obtuse compared to something like redux-first-router.