"Nobody can "just assert dominance over all Muslims," since there is no structure, no heirarchy, no pecking order in Islam."

Is that "in theory"? Certainly not in practice (I mean the bit about a "pecking order")

The self-styled Grand Mufti of Jerusalem who set the Arabs against the Jews and worked damned hard at keeping that pot boiling for his entire life.

The 12 Old Gits and the Ayatollah in Iran certainly make strides in their assertion of their dominance over their Muslims

Al-Sistani in Iraq and the Shia of Iraq.

And now al-Baghdadi of ISIS or ISIL or whatever you want to call it.

It should be handy having them all gather inside their Caliphate - any trouble - declare it the largest live firing range in the world.