The mediterranean world was indeed an amazingly prosperous place for thousands of years: The mediterranean is a mellow sea whose trade routes facilitated trade and interconnectivity, fostered prosperity, and even transported institutional innovations.

However, very little of that has any impact on modern economic growth and ability of a state to project power.

Or rather, in a way it does but not in the way that would have helped North Africa (or any part of the Mediterranean really) achieve the sort of institutional set up which resembles what we would recognize as a nation being “Rich and Powerful.” Almost all modern economic growth is industrial growth (you can technically leapfrog directly to service-sector growth, but it’s very difficult) and there is no Mediterranean country which fits the criteria for early industrialization as it instead existed in Northwestern Europe. I wrote a bit about that from a different lens in this older answer which might interest you. In short, the institutions which developed in Western Europe were particularly well-poised for political power projection on one side, and fostering economic growth in the other side. And while they did absorb institutional principles which originated from the mediterranean, they molded them such that they could foster we would consider successful outcomes (from a pure point of view of economic development and power projection).

In a way, North Africa did benefit from being in the Mediterranean Basin and from the post-Roman heritage which survived in its cities. North Africa is more urbanized and more prosperous (on average, twice as prosperous to this day in pro-capita GDP terms!) than the rest of the continent. Is it really “Off the Cultural Map?” I’d respond, “Who’s cultural map are we talking about?” North Africa was an important component of the Ottoman Empire, but even before then, in the centuries prior the Emirs of North Africa were important players in Mediterranean politics. One might even call the North African Emirs the dominant players in the region for hundreds of years, developing powerful Caliphates like the Umayyads who had western Europe on the back foot for much of their history. And while North Africa's role in mediterranean power politics would slowly decline from around the 12th-century on, it's only after Europe industrialized that European Powers exerted any sort of real colonial dominance or any sort of policy over North Africa (which you can imagine, once they did manage to do so, ultimately wasn't exactly a helpful experience in economic development). After decolonization, North Africa went on to again become an important cultural exporter: While the region’s aridity meant that it is generally can support smaller cities compared to the other bank of the Mediterranean (also contributing, perhaps, to its lessened prosperity; keep in mind that until the industrial era, the main economic activity anywhere was agriculture), the fertile Nile floodplain makes Egypt an important exception: Egypt is a large and densely populated country (and prosperous too, in relative terms: it is the second-largest African economy and the ninth-most prosperous in per-capita terms) with the ultimate effect of creating a large media market. As a consequence, since the 1950s the Egyptian film and television industry became a massive exporter of “Cultural” content like films and TV-shows, especially to the Arabic-speaking world (I consider myself a bit of a film history buff - I thought I had written an answer on the Egyptian film industry at some point, but I can't find it anywhere. I'll go back and link it if I find it).