According to Mormon doctrine, Resurrected beings have physical bodies that can only be in one place at one time, which is why the Holy Ghost remains a spirit, so that he can dwell in the hearts of men:
"The Father has a body of flesh and bones as tangible as man’s; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit. Were it not so, the Holy Ghost could not dwell in us." (D&C 130:22, emphasis added)
It appears to me that some form of power or ability is lost at the resurrection. An essential power that only spirits have, which resurrected beings do not, hence the necessity of the Holy Ghost remaining a spirit.
It seems somewhat paradoxical to me that we would have anything to lose at the resurrection–if anyone understands what I'm trying to communicate by phrasing it that way... Obviously the Holy Ghost is going to be resurrected at some point (I feel it's safe to assume so at least), at which point in time he will forfeit the power that makes his role in the Godhead essential, and receive a resurrected body. My question is, what exactly is this power that the Father and Christ cannot wield as resurrected beings? Or where do I err in my pondering or phrasing of my question?