Yep, this is a problem I’ve encountered several times. Even if none of your own code has unhandled throws, you’ll inevitably get crash reports coming in from fooLib throwing an exception somewhere because the moon was in the wrong phase.
There are entire languages built with unchecked exceptions, Python, Ruby, Nodejs and most recent ones. Even with checked exceptions you can write code and miss to throw or declare an exception somewhere so ultimately the developer has to deal with exceptions somehow.
I also am extremely unhappy that those functions can be 16 layers deep somewhere in a lib and cause your app to blowup.