You should catch any non specific exception in the last catch block, just in case. Thought that was the standard. Java gets very messy in mixing checked and unchecked exceptions, I've seen a lot of devs just ignore the unchecked ones.
I’ve seen too much code were some random problem in an Error - OutOfMemoryError for example when processing too much data (Eg call data records, payment records, analytic records, whatever). If it’s a batch processing job, you don’t want this problem for this specific entity causing the rest of your reports not to be sent.
I’ve also seen stupid things like RPC libraries silently swallow Errors and not report them properly to the caller, so we end up wrapping all RPC server endpoint methods in a try-catch-Throwable just so we can see the problem and log it.
If I’m processing a monthly report for millions of customers, I don’t want to abort processing after running into one problem customer. I want to continue to process the rest of them, and log the problem customers exception for troubleshooting and analysis offline.