Q:

Could the vision of Star Wars's galactic core worlds be even remotely plausible

From my, albeit limited, understanding, the galactic core is nothing more than super-massive black holes where nothing has absolutely any chance of living, ever. Yet in Star Wars, the core worlds and, if I'm not mistaken, deep core worlds  are the most rich and prosperous of worlds.
What I do understand is that you do want to be somewhere in the "middle" area of the galaxy. Everything is closer by and there is more of everything. All worlds here, provided they are class M (or any other class that would be perfect for some sort of life-form) would be incredibly favored compared to outer rim worlds.
But the question is: Could worlds very near the core actually be livable ? How about within the core ?

A:

According to the maps seen in Star Wars: The Essential Atlas, the "core" worlds are those that are relatively close to the Galactic core. Their wealth comes not only from mineral wealth but also the relative ease of travel (multiple major hyperspace routes have been plotted between them) and the relatively short distances between them, facilitating high volumes of commerce.
Note that in the original Star Wars Atlas maps, within the core proper (described as the "deep core") there were no listed planets. The latest version of this map, however, adds a few planets that seem to exist well within the deep core.

Star Wars: Atlas (non-Canon)

Star Wars: Updated Atlas (Canon)

