One big caveat concerning DI. Except of simply measuring political freedoms, it measures also quality of governance and political culture, so enlightened authoritarianism in Singapore counts as "flawed democracy". After seeing that my country (Poland) scores lower than South Africa, I have problems to take it fully seriously.
1) Democracy, in its modern form is a Western invention and we're grading such countries according to Western expectations, and even by Western own standards it works really well only in Germanic countries. When it had to be transplanted in to a different cultural background, it's usually bundled with other "suspicious ideas" (like secularism, women rights) it may be a bit hard sell in Arab world.
(for arguments sake we could construct some, let's call it "Confucian index" and grade countries whether their governance structure is properly meritocratic and technocratic, top western democracies would score reasonably well, but nothing breathtaking)
2) Clan society - According to Fukuyama's origin of political order, Roman Catholic Church disassembled tribal society by curbing cousin marriages (Sure, one could buy indulgences, but they are not cheap...). Simultaneously Islam approves them, thus remnants of clan society exist.
3) It's not exactly Islam as such (Iran and Indonesia seems not be dragged down), but in Muslim Arab culture there seems to be something against good organisation and intellectualism. It manifests itself in multiple ways, starting from high corruption, low number of books published or even poor military performance of otherwise seemingly well equipped and high morale armies (Americans are surprised by high losses of Abrams tanks by Saudi Arabia in Yemen, Soviets were shocked how Syrians were failing to deploy correctly SAM batteries against Israel)