All exceptions must be checked exceptions.
Unchecked exceptions are unrestricted gotos. And unrestricted gotos are considered a bad thing.
Unchecked exceptions break encapsulation. To process them correctly, all the functions in the call tree between the thrower and the catcher must be known to avoid bugs.
Exceptions are errors in the function that throws them but not errors in the function that processes them. The purpose of exceptions is to give the program a second chance by deferring the decision of whether it's an error or not to another context. It's only in the other context can the correct decision be made.