usemap in XHTML 1.1 no longer a URI?!

I've been trying to figure out why one of my sites no longer validates when I switch from the XHTML 1.0 strict dtd to the 1.1 dtd. Someone pointed me to a posting that pointed out the datatype for usemap had changed from URI to IDREF.

Poking around in the 1.1 DTD, I found this to be true, and also found this, which explains the change:

<!-- 'usemap' points to the 'id' attribute of a <map> element,
     which must be in the same document; support for external
     document maps was not widely supported in HTML and is
     eliminated in XHTML.

     It is considered an error for the element pointed to by
     a usemap IDREF to occur in anything but a <map> element.
-->

Can anyone tell me why this was done? It makes it impossible to write a valid XHTML 1.1 document that uses an image map (at least if you want it to work in today's browsers).

I thought the whole point of XHTML was to be backward compatible, and I have found nearly every other single aspect of XHTML to allow that. Why is this different?

How do I get around this problem?