As title says, reading through classic historiography from medieval and early modern history I get the impression that the Islamic world has far less to offer when it comes down to documents. What I don’t really know is if that’s only because classic western authors couldn’t or didn’t bothered to try to learn Arabic or because there really isn’t that much of a documental tradition in the Islamic world.
You're partially right -- it wasn't until after WWII that European historians really started learning Arabic and looking for documents. Even Fernan Braudel's The Mediterranean In the Age of Phillip II, which was the first major work to consider both sides of the Mediterranean as intrinsically linked relied primarily on European sources for North African and Eastern Mediterranean history.
The big problem isn't that documents weren't kept -- Islamic dynasties thrived on paper and bureaucracy; the Ottomans, for example, were extensive record keepers; so were the various dynasties that ruled Egypt -- but that the states that inherited them haven't cataloged their archives and don't tend to allow researchers in, so no one can really be sure what they do and don't have.
The Turkish republic, for example, only opened the Ottoman archives in the 1960s; the Egyptian national archives were scattered all over Cairo in various places until around the same time; even now they're infamously (well, among Egyptian historians) poorly organized and safeguarded behind closed doors, and access to foreign researchers is, once again, very difficult to gain.
So, it's really more that scholars have to make do with what they can get. Myself, I wrote my entire doctoral dissertation on Egypt with material I could find in London and what I could access online from the 19th century because I couldn't get clearance to work in Egypt -- pity the poor folks that want to work on Syria, or Iraq, or Iran right now, too...