I'm sure but I going to be called a deflectionist here but is that not the same issue with most religions?
My initial thought when reading about the lack of a central leader was to agree with you, but then subsequently I don't think it's quite as clear cut as you're making out. Yes Catholicism has a central figure, but he is only the central figure for one of the many religious denominations that make up Christianity. When you don't agree with his interpretation you split and make up another denomination - see the CoE as a prime example. There are many denominations of Christianity all the way down to the Wesrboro baptist church, all technically worshiping the same god and history, but interpreting the bible in different ways - some literally, some figuratively and some just picking and choosing depending on what they want to portray.
Some take the less savoury paragraphs and claim they should be followed literally, while most moderate people (and denominations) realise they aren't fit for today's world and just don't teach them (as Dis pointed out in his post). Doesn't matter if those paragraphs are in the Koran or Bible.
That's what we see in Islam - Shia and Sunni being the two biggest denominations, both having very different interpretations of the book that is apparently not interpretable. We see this throughout the religious world, heck, not even the religious world, the world as a whole - it's basically the premise of countries as well.
Not having a central leader doesn't help matters (depending on what they are preaching), but it's not the "structural problem". If Islam had an "supreme" leader how would that change what we see today? I don't think it would change much - those wanting to use their interpretation of Islam as a weapon would just split (or be thrown out) and create their own denomination with their own leader and followers believing their interpretation was the correct one.
There are a whole host of reasons for the current issues with Islamists but I don't think a lack of leadership or any particular structural issue is any more an endemic problem than in any other religion.
I think your last paragraph hit it on the head, it's all about greed, power and control in its various forms. Either using religion as a weapon to unite people to their cause, or as an identifier in their differences.
Take for example the fight Scorza brought up in the Philippines. The Islamic insurgency in Mindanou. It's been going on for hundreds of years and essentially started as a independence battle between Muslim communities and the Spanish empire insisting their lands belonged to them and that they would have to convert to Christianity when they colonized the Philippines (subsequently the Americans tried the same thing). It's essentially been a seperatist battle with a bit of cultural heritage thrown in.
Other organizations like ISIS and Al Qaeda are all about trying to "protect" what they perceive is their culture from outside interference from others - largely western culture, which is a major influence on people throughout the Middle East and North Africa (and most of the rest of the world). They're dinosaurs trying to hold on to what they believe was golden era, using religion to entice followers to their cause. They then use violence to try and implement that change, and then force people to live in the way they believe is right (see their actions against those unfortunate enough to be stuck in cities under their influence), no difference to any other extreme right (or left) wing organization.
Islam is perfectly happy coexisting in a modern democratic society, as seen by the millions of Muslims living peacefully in them. Much of the current day issues are due to a multitude of historic and current day events, no more to do with religion than any other.