Simply put: Either the Guard is a state militia that’s only part of the United States Military when called to national service–in which case it has no business on the Joint Staff–or it’s a part of the Total Force and therefore already represented on the Joint Staff by the Chiefs of Staff of the Army and Air Force. (There is no Navy or Marine Guard.)
The former was the traditional view of the Guard; the latter was pushed after the post-Cold War drawdown necessitated more frequent utilization of the Guard and Reserve for routine missions. As late as Desert Storm, the Guard was widely viewed as a joke by the Active force, at least in the Army. While certain specialty units in the Reserve were called up, only a handful of Guard units were and none was deemed ready to deploy to theater by war’s end.
Over the last twenty years–and certainly since the wars in Afghanistan and Iraq kicked off in 2001 and 2003, respectively–the old norm became obsolete. The operations tempo has simply been too high to sustain with a relatively small active force. Guard and Reserve personnel have been deployed routinely and are more-or-less indistinguishable from their Active counterparts.