I don't disagree with Paarthurnax trying to claim control over his kin with Alduin gone, as Odahviing said, "the tyranny of Paarthurnax's Way of the Voice", but I find it very unlikely he's going for a Dragon Cult.

However, all except Miraak (guided by Hermaeous Mora) probably did not know they had this potential.  

Huh, now isn't that an interesting thought? Imagine the dragons elevating the priests into positions of great power because they knew the Dragonborn Priests were their biggest threat. One must keep friends close and enemies even closer

Who knows the secret?

Kind of puts Hermaeus Mora and his schemes back in focus doesn't it? Like, the whole Dragon War, Alduin and everything that happened since could be traced back to Mora revealing to Miraak his true power...

This is far fetched but worth a thought:

He tried domination by might but it didn't work. Maybe domination by peace will?

Is that something to object to?

Sorry in advance for such a long comment . . . 

Imagine the dragons elevating the priests into positions of great power because they knew the Dragonborn Priests were their biggest threat. One must keep friends close and enemies even closer

This is very true and has interesting implications. Did the dragons truly know of the dragonborn's full, soul-absorbing power? Could it be that they only sensed that the dragonborns had powerful potential, so the dragons elevated the priests to a position where they could be "monitored"? It seems to me that a dragon wouldn't know the dragonborn's true power until Miraak started killing dragons and absorbing their souls. If we assume that all priests were dragonborn, and we further assume that the dragon cult was initially peaceful and not corrupt, then we should also be able to safely assume that the idea of killing dragons (and absorbing their souls) would have been abhorrent to a society that revered/worshiped dragons. This is probably why the Solstheim dragon priests (namely, Vahlok) fought against Miraak instead of emulating or joining him.

It also sheds further light on the Dragon Rising mission. Just as you defeat him, Mirmulnir will shout, "Dovahkiin, No!" Was he surprised/shocked or angry? Then, during A Blade in the Dark, we get this dialog (from UESP):

• Alduin: Ful, losei Dovahkiin? Zu'u koraav nid nol dov do hi.
  • So, my false Dragonborn? I do not recognize you as dragon. (So, my of-fake Dragonborn? I recognize no from dragon of you.)
• Alduin: You do not even know our tongue, do you? Such arrogance, to dare take for yourself the name of Dovah)

Interesting implications . . . Which brings me to good ole Mora. Did Miraak discover his soul-absorbing ability on his own or did H. Mora tell him (in conjunction with the Bend Will shout)? What was H.Mora's angle in all this? He certainly has a propensity to screw around with Nordic affairs (i.e., almost transforming them into Aldmer; he seems to have a thing with Ysgramor). 

If we assume that all priests were dragonborn, and we further assume that the dragon cult was initially peaceful and not corrupt, then we should also be able to safely assume that the idea of killing dragons (and absorbing their souls) would have been abhorrent to a society that revered/worshiped dragons

Well said, much clearer than how I put it.

What was H Mora's angle in all this?

This is where it gets interesting. The book Imperial Census of Daedra Lords says this:

Hermaeus Mora, “the Gardener of Men”, claims that he is one of the oldest Princes, born of thrown-away ideas used during the creation of mortality in the Mundus. Imperial Mananauts have verified that his influence on fate and time is real and unfeigned, implications of which tie this Prince directly with Akatosh, chief of the Nine Divines.

Now, it must be remembered that this book doesn't appear in game. However this book is referenced (or references) another book which does appear in ESO.

Hard to answer. At what point in evolution do you start judging an animal by its behaviour? See, anything that limits the natural behaviour of any creature is questionable to me unless it serves the greater good. De-clawing a cat because it scratches the furniture , for example, is cruel. A cat will scratch - it's what they do.

My cat could go and kill numerous mice and birds yet not eat them, playing and tormenting them before their end. I do not consider the cat bad for it is doing what is in its nature.

The same behaviour from a human is abhorrent because it's not in our nature and we can and should exercise self control over everything we do.

Such behaviour is in a dragon's nature but they are more intelligent than us and so should be held accountable for their actions too. Yet the will to dominate is in their blood for that is how they were made.

Paarthurnax is the only one who has succeeded but even that success is slightly tarnished by our suspicion of his true motives.

I don't think he's necessarily going for a Dragon Cult either, but the result could come with the same consequences.

He already has a mini cult dedicated to him, albeit with only four members.