React passing down hooks causes rerender and loss of focus on input

I’ve got a parent component in which I initialize some piece of state, which I then pass down to the children components so that they can update that. However, when the update is triggered, the component tree is re-rendered and my inputs lose focus. Adding a key did not help.

// App.tsx

export function App(props) {
  const useVal = useState("");

  return (
    <Router>
      <Switch>
        <Route
          exact
          path="/"
          component={() => (
            <StartScreen
              useVal={useVal}
            />
          )}
        />
        // ...
    </Router>
  );
}

// StartScreen.tsx

interface StartScreenProps {
  useVal: [string, React.Dispatch<React.SetStateAction<string>>];
}

function bindState<T>(
  [value, setState]: [T, React.Dispatch<React.SetStateAction<T>>]
) {
  return {
    value,
    onChange: ({ value }: { value: T }) => setState(value)
  }
}

export const StartScreen = (props: StartScreenProps) => {
  return (
    <form>
      <InputField
        key="myInput"
        {...bindState(props.useVal)}
      />
    </form>
  );
}

So, now when I start typing on my InputField (which is basically a wrapper on an <input>) on StartScreen.tsx, the input constantly loses focus as the component is totally re-rendered (I can see it in the DOM).