Is the matter about Mohammed's successors really that important?
It's about as important as the matter of Mohammed being the "successor" of Jesus Christ, and Jesus Christ being the "successor" of Moses, and Moses being the "successor" of Abraham, and Abraham being the "successor" of Noah, and so on all the way to Adam and Eve. In other words, it's not important at all.
Alas, people are fighting over such matters all the time. The most stupid wars of history were provoked by religious considerations.
I am with you when you say that a theocratic government is ineffective in the modern world. Not that religion and modernity are totally at odds with one-another, but religion isn't the way to run an entire country. More generally, any ideological government is inconsistent with demands of the modern world.