Why can't I access the Screen.ids?

kv rules are not applied until the original Widget has finished instantiating. In this case, your Manager widget is the initial widget - it, in turn, creates the other widgets including RootWidget. This means that in your RootWidget.__init__ the ids are not yet populated! They will be as soon as Manager finishes instantiating - so the best approach is to just delay the rest of your initialization, like so:

class RootWidget(Screen):
    def __init__(self, **kwargs):
        super(RootWidget, self).__init__(**kwargs)
        Clock.schedule_once(self._finish_init)

    def _finish_init(self, dt):
        self.grid = self.ids.grid
        # etc