If it only works when you write the types correctly with no mistakes, what's the point? I thought the point of all this strong typing stuff was to detect mistakes.

Because adding types adds constraints across the codebase that detect a broader set of mistakes. It's like saying what's the point of putting seatbelts into a car if they only work when you're wearing them - yes you can use them wrong (perhaps even unknowingly), but the overall benefit is much greater. On balance I find that TypeScript gives me huge benefit.