Proposed resolution:

Change [iostream.objects]/1:

-2- The objects are constructed and the associations are established at some time prior to or during the first time an object of class ios_base::Init is constructed, and in any case before the body of main begins execution.²⁹⁰⁾ The objects are not destroyed during program execution.²⁹¹⁾ If a translation unit includes <iostream> or explicitly constructs an ios_base::Init object, these stream objects shall be constructed before dynamic initialization of non-local objects defined later in that translation unit, and these stream objects shall be destroyed after the destruction of dynamically initialized non-local objects defined later in that translation unit.

lib.iostream.objects requires that the standard stream objects are never destroyed, and it requires that they be destroyed.

DR 369 adds words to say that we really mean for ios_base::Init objects to force construction of standard stream objects. It ends, though, with the phrase "these stream objects shall be destroyed after the destruction of dynamically ...". However, the rule for destruction is stated in the standard: "The objects are not destroyed during program execution."