To my mind the big issue with existing examples of checked exceptions is that the language to talk about the exceptions is woefully inadequate, so it stops you

To my mind the big issue with existing examples of checked exceptions is that the language to talk about the exceptions is woefully inadequate, so it stops you from writing things that would be useful while dealing correctly with exceptions. The go-to example is a map function, which we should be able to declare as throwing anything that might be thrown by its argument. Without that we need to either say that map might throw anything and then handle cases that actually can't happen, suppress/collect exceptions inside map, or suppress/collect errors inside the functions we're passing to map, all of which add boilerplate and some of which add imprecision or incorrectness. It would also be good to be able to state that a function handles some exceptions if they are thrown by its argument. And all of this should be able to be composed arbitrarily. And... somehow not be too complicated. For usability, it should probably also be possible to infer what's thrown for functions that are not part of an external API.