Why is a sorrowing heart called "Sultan" and a stone heart called "burial site" in this verse of Saint Kabir?

Here's a translation that I think captures the literal sense better:

Don't call (the pain of) separation bad; it is king. A body that doesn't suffer (the pain of) separation is always a graveyard.

"घट / ghaT" is literally a clay pot. In Kabir, it's a common metaphor for a person's body, in the sense of physical frame (not corpse).

"बिरहा / birahaa" literally means separation but connotes the pain one feels at being parted from a loved one. Kabir says that although we consider being parted from a loved one something bad, undergoing that pain is a sign that our love is alive, and so we should honor that pain the way we honor a king.

If we did not undergo this pain, then the person we are parted from is absent not just physically, but also from our emotions. That makes the absent person effectively dead to us. Since they no longer live in our hearts, our hearts are their graveyard.

This दोहा / dohaa, couplet, of Kabir's exemplifies the tremendous philosophical, psychological, and emotional insight he is celebrated for being able to pack in just two lines:

• Emotionally, if two lovers are separated, each of them does suffer the pangs of separation. Kabir says this is in fact a sign that their love is true, and that if they did not feel such pangs, their love is dead.
• Psychologically, this couplet also serves as consolation to those who are bereaved. Kabir points out that a bereaved person's grief honors the dead person, and keeps that person alive. If the survivor didn't feel such grief, then the person would be truly dead, and the survivor would be that person's eternal graveyard.
• Philosophically, this couplet is about the individual soul's yearning for union with God. Kabir was at once hard-headed and a mystic; his poetry is antiromantic while being deeply spiritual. He says that our awareness of our distance from God is something that should rule over us like a king. If we lose sight of that awareness, then we are eternally dead in every way that matters.

Further, when Kabir says that birahaa is सुलतान / sultaan, a sultan, that characterization is doing double duty. On the one hand, he's acknowledging that grief is often overmastering, and does rule our emotions as a king would. On the other, he's also saying grief should be honored as a king. Our actions should be governed by our sense of separation from God the way subjects are governed by a king. As always in Kabir, there's a didactic or ethical precept underlying his poetry.

So feeling the pangs of separation is what keeps our love, our loved ones, and our relationship to God alive. If we don't feel them, then all those are dead, and our bodies are just graveyards.

Note: transliterations from Hindi in the question and the answer follow iTrans conventions.