Should user input be able to cause an unhandled exception?
No, user input shoulnd't cause and unhandled exception. Not only because is a nasty reponse form server but it reveals an error condition not handled so it may head to security issues. A non-handled error means that developers are not aware of that error (or they are too lazy, what may be worst).

All error conditions should be handled to minimize problems related to that uncontrolled error.

I've tried to reproduce the bug (with two input name fields with name="name[]" as you have shown in your images) without getting reported error. So I think this
particular case you mention seems to be a drupal.org bug or a module bug of a module used in the Drupal site. You can report the bug in the Drupal.org infrastructure issue queue