Although submarines are more effective navigating through storms, one could simply wait for the storm to pass when shipping non-time-sensitive cargo, then use a regular surface cargo ship (which could be automated if desired just like the submarine). Surface ships also have the advantage of compatibility with our already-established shipbuilding and maintenance infrastructure, while a submarine would require the proliferation of new skills and tools to support it.
For time-critical cargo (where one can't wait for a hypothetical storm to pass), it's likely aircraft would be a better option for most shipments - certainly in severe storms aircraft can't operate either, but in that case the very act of loading and unloading the submarine would be hazardous as well.