I'd say in many cases it is perfectly desired to either swallow or re-throw exceptions. As just one example, many business rules can be correctly implemented as best-effort and if some resource (network or service) is unavailable simply let the failure propogate, or log, or backoff and retry some other time.
And most certainly but in fewer cases more robust handling is called for. Even if only 10% of exception handling is in this category, then try/catch is still a valuable tool.
I find it really faulty to reason that "this feature is only used 'correctly' 10% of the time, therefore it's a failed feature."