The Abbasid era tends to be thought of as the golden age because of the Dār al-Hikma (House of Wisdom) in Baghdad and the scientific thought that took place there; it was also the era of rulers celebrated in the Arabian Nights, especially the Khalifa (Caliph) Harun al-Rashid. Also lots of poetry, art, and etiquette manuals came out of the Abbasid state.

It is...to be honest...not an entirely fair designation. As you point out, the Abbasids were pretty bad at holding territory. There was just as much scientific output in Cairo under the Fatimids (and their successors, the Mamluks), and from Samarkand under the Timurids, and from Fez, and Córdoba, and Istanbul, and Delhi, and...you get the picture.

I think one of the reasons the Abbasid era is held up so much is that it was the last Islamic state to rule a unified territory before areas started to splinter off (this is, historically, debatable, but it’s how it’s remembered). I mean, at one point during the Abbasid era there were three caliphs: theirs, the Fatimids, and the Umayyads in Spain.

What we can say the Abbasids left is that under their rule, what we come to think of as ‘normative’ Sunni Islam really took shape. The four main schools of law were crystallized, the systems of jurisprudence (Islamic legal studies, which really encompasses all forms of education—even the hard sciences were technically a specialization within religious education) and how people were trained in them took shape, and this was then spread outward—ironically, in order to counter the rival Fatimids, who, as a Shi’a dynasty, left very little trace of their two centuries of rule on Egypt, whose Muslim population is 99.9% Sunni.

It’s a bit like how Shakespearean and Elizabethan England has something of a storied place in English history, even though there’s so much more of it than that (and, if you get into the details, it wasn’t a particularly pleasant time or place to live).