Should you report the message text of exceptions?

Consider some code that can throw a checked exception (an exception of type Exception). Your code catches the exception, of course. You don't just swallow the exception either, your code reports it in some way to the user through your user interface. In a log file, perhaps, or using a GUI pop-up.

Should the text you report to the user include the message text of the exception. That is, the text provided by Throwable.getMessage() or Throwable.getLocalizedMessage()?

I think not, but it seems many disagree with me. So what have I got wrong? My argument is as follows.

• The message was created when the exception was thrown. It therefore at best can provide only very low level information, which can be inappropriate for reporting to a user.
• Philosophically, using the message seems to me against the whole point of exceptions, which is to separate the detection and initiation of error handling (the throw part) from completion of handling and reporting (the catch part). Using the message means the message must be good for reporting, which moves responsibility for reporting to the location that should be responsible for only detection and initiation. That is, I'd argue that the getMessage() part of the design of Throwable was a mistake.
• The message is not localised. Despite its name, getLocalizedMessage() is not much good because you might not know what locale you want to use until you catch the exception (is the report to go to a s