None of those arguments are convincing. In many cases, you can't handle errors more reasonably than just crashing or telling the user something went wrong. Java has RuntimeExceptions, which do not have to be declared in the function signature. Division by zero, or trying to index an array out of bounds, and the dreaded NullPointerException, are some examples of RuntimeExceptions.
You usually wouldn’t crash the entire application, the request that causes the issue will return a 500 error. (Or equivalents for non-web environments.)
Some exceptions are not recoverable and may cause 500 error. Others such as FileNotFound are recoverable, for example by reading the file from an alternate location.
