I think you have to distinguish between two scenarios when faced with sudden road closures.
On minor roads, you can try to bypass the closure ‘by sight’. It’s not the most elegant solution, but it’s doable.
On the motorway, this is more difficult, as the map showing the route scrolls off the small display. If the app now wants to divert me at the next exit, I don’t know whether it’s trying to take me back or whether that’s a way back onto the route (somewhere past the closure).
That’s why I think it’s so important to be able to mark a closure in some way (e.g. by pressing a button), so that the app definitely doesn’t try to take that exit again.