Then I don't see how you can claim that the fact that "Promises coerce caught exceptions occurring on the origin tick to errors" is bad. This coerces all the invalid argument exceptions into errors. Is that bad? Or are there other errors which should not be caught but are thrown in this manner, and if so, can you provide (links to) examples which ones and why?

These should be quite rare and are addressable by wrapping that badly behaving function with a crashy wrapper that throws asynchronously...