XHTML closing tags

As I understand it, this is how it MUST be done:
<TAGNAME>xxxxxx</TAGNAME>

But why is:

<TAGNAME>xxxxxx</>

not valid?

I can see several benefits:
The strict nesting rules will be automatically implemented.
The editor/viewer will have no problem figuring out which closing-tagname to
display, if the user wants that.
It saves a lot of volume, when transmitting/storing files

kind regards,
Matthijs Mullender